multi-period consumption and investment decisions under

35

Upload: hahanh

Post on 11-Feb-2017

216 views

Category:

Documents


1 download

TRANSCRIPT

Page 1: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

� ��������� � ������� �������������������� ����� � �"!#�$�%���&� �'�()�$*+���,�������-������� � ./��*+� �0�1�����'�32 45�6!#�����7��� � 8

9�:<;>=@?�A�BDCFEGEF?IHJ;K:<AMLONPRQTSVU�WYXYZ1Q[\X,]_^a`cbK]d[e]dZgfhbTi

jkflQmlQT^FQmon pq[rfls_QTWtiYfoXvuwyx{z|x}j%]7~��T�_�$����

PR���_�_���e�DjkflQmoQT^GQmon��r��QTWtZgU_[\uZgU�WYX�Q[�x��rfomomlQT�}WtU_[rnV���}[rf����}flQm�QT^FQmonOx�n�Q

��:<A"��?�AJ�I?�EFHM�J;@��?I;� Q[\X�WYQ�^F]_W�`cbK]d[r]dZgfob���Qi�QU�Wtbt�

��QTQmlQ�pq[rfls_QTW>iYflXvu��QTQmlQ_�M�����1��j,�|�MpR�

�Tx¡ %Q[e¢TQml�}�eWt£_QTW@�qQbK]d[Ox¡¤_QTQmlQ_x�U_b�x��r¤

¥§¦�¨k©«ª ¬§¬a­

®�¯±°d²V¦�°d°d¯±³y¨µ´·¶¹¸q©}º'»�³�¼R½ ¾a­

¿�ÀyÁTÂ7Ã�ÄrÅ_Â�,�}foi�S}U�SJQTWÆi�XY�}nrflQi�XY�eQ·bK]d[riY�rZ1S}XYfl]d[��vfo[\s_Qi�XYZ1Q[\X�SrWY]_�VmlQZÇ]_^,U$bK]d[riY�}Z1QTWÆ �foXY�

UÈZ|�rmlXYfl��SMQTW>fl]<n3S}mhU_[r[rfo[e£É�e]_Wtfo¢T]d[��r[rnrQTWÆ�r[rbKQTWYXYU_fh[ÊX�u_x$�e�rbt�'UËi�QTX�XYfo[e£È]<bTbT�eW>iÆ[rU�XY���WtU_momou·fo[ i�X�]�bt�}U_i�XYfob|z�Ìy�ÍZ1]�neQmoik RflXY�$Z|�rmlXYf���SJQTWtfl]�n��vmofos_Qn6bK]d[riY�}Z1QTWtiTxÏÎ"QÆSrWY]7s�foneQ�UWtfl£_]_Wt]d�riRb>�rU�WtU_bKX�QTWtfo¢U�XYfl]d["]_^�bK]d[}iY�rZ1SrXYfo]d[��vfo[\s_Qi�XYZ1Q[\Xqi�X�W>U�X�QT£dflQi��r[rneQTWq£_Q[eQTWtU_m§U_iÐ�iY�rZgSrXYfl]d[ri§]d[6SrWYQT^FQTWYQ[rbKQicU_[}ngQK~�SMQbKXYU�XYfo]d[ri�U_[}ngneQTWtfls_QRbK]d[rnrflXYfl]d[}ia^G]_W�XY�eQ,QK~efoi�X�Q[rbKQ]_^cU_[3]_SrXYfoZ6U_m i�X�W>U�X�QT£_u_xÆ�,�eQDSrWY]_SJQTWYXYflQiR]_^ÏXY�eQ|WYQiY�rmoXYfo[e£6neQZ6U_[rnÈ^Ñ�r[rbKXYfo]d[riRU�WtQ0fh[��s_Qi�XYfl£dU�X�Qn�fh[�£_Q[eQTW>U_m%U_i0 %Qmom%U_i|^G]_W0XY�eQ�SJ]_S}�rmoU�W|bTU_i�QÉ �flXY��bK]d[}i�XYU_[ÊX1WtQmoU�XYfls_Q�Wtfoi�¤Us_QTW>iYfl]d[�Ò � ����Ó�Ô>x

Õ1?IÖr×qØ<;@LJÙIÚ 9��JEh=KCoÛ�ܹ?�;@CGØVL�ÜJEÑ:\AJAJCFAM�+ÝJØ�;>CF��Ø<A§Þ§ß�Ø<AJÙ@�JàÈÜM=@CFØ�A�CGArá<?�Ùt=KàÈ?�Ae=gÙ>=@;K:\=@?���CG?�Ù�ÞaܹØ�;t=>Ûâ Ø�EGCFØÉLJ?Iß�CGÙ@CFØ<AJÙ�ÞOÙt=KØ}ßTÝO:<Ù>=@CFßgLMÖ}AO:<àÈCFß1ÜM;@Ø���;@:<àÈàËCGAJ�JÞrÜJ;@CGAJß�CGÜJEF?|Ø â Ø<ÜM=KCGà3:<EGCG=�Ö<ã

��ä,åçæqEÑ:<Ù>Ù@ChèOß�:\=@CFØ�AyÚ é$ê<ê�ÞOëÉê�ê�ÞJë1ìMêí@î ïñðñò_ó�ôGïñð�î õ÷ö>øIù�õhótúYûÑü÷ü÷ý±þYòlÿÐî ðIó�ôGï�ðñî õ÷ö>ø����ÐöÐô\ûÑü÷ü���ú������ ����������������� ���� �"!$#&%'!)(+*-,�!/.10'!2,30'4 56487:98!2%;=<48>�?A@CBD7:#&EGF�HI>�?J(K0'LM#&*-,ONP>-48%IQ�0'!/*SR6#&?JT�!/76EU4V%

?)#&*XWM,�(:Q'HZY-Q'Q[(+4V*-Q/\]Z^ 4V%[%'!2Q[T_4V*-,1(:*�`a#8Y10[>-48%�\�N�!/7b\:cedDfVg)h8i�jaj�k8lafVm8n�h1\

Page 2: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

������������� �������

��ÝJ?'Ù>=@�JLMÖçØ â àÉ�MEG=KCoÛ�ܹ?�;>CFØ}L�ßIØ�AJÙ@�MàËÜM=@CFØ�A}Û�CFAeá<?�Ù>=@àË?IAe=$ÜJ;@Ø�HMEF?�àÈÙÉÝO:\ÙÈH¹?�?IAç=KÝJ?"Ù>�JH��>?�ß7=3Ø âAr�JàË?I;@Ø��MÙ�Ù>=K�MLJCF?IÙ�CFA+=KÝM?1EFCG=@?�;@:\=K�J;>?<ã%� ÝMCFEF?Æ=KÝJ?1?IàËÜMEFØ_Ö�?IL�Ù>?I=>=KCFAM��Ù�:<AJL�:<Ù>Ù@�JàÈÜM=@CFØ�AJÙqLJC�� ?�;ß�Ø�AMÙ@CFLM?�;K:\HJEGÖ<Þ�:\EFEkßIØ�Ae=K;@CGHJ�M=@CFØ�AJÙgÙ>ÝO:<;@? =@ÝJ?ËßIØ�àÈàËØ�A�Ø<H��>?�ß7=KCGá<?È=@Ø�Ø��y?I;·:'Ù@Ø<�JAJL àËCGß�;@Ø}?�ßIØ\ÛAJØ�àÈCFß â Ø<�JAJLO:\=@CFØ�A Ø â =KÝM?�LM?�ß�CGÙ@CGØ�A H ?IÝO:�áVCGØ�;$Ø â CFAeá�?IÙ>=KØ<;@Ù$×�CG=KÝ àÉ�MEG=KCoÛ�ܹ?�;>CFØ}L EFChá�?IÙ CFAç=KÝJ?ÜJ;@?IÙ@?IAJß�?0Ø â �JAJßI?�;t=T:<CGAr=�ÖÈLJ�M?Æ=@Ø�Ù>=@ØVßTÝJ:<Ù>=@CFßÆCFAeá�?IÙ>=KàÈ?�Ae=q;@?I=@�J;@AMÙ�ã��V�JßTÝ+:6Ù>?I=@=@CFAJ�·ØVßIß��J;>ÙRAJ:\=>Û�J;K:\EFEGÖ$CGA+àË:<AeÖË?Iß�Ø�AMØ�àËCGß|àÈØVLM?�EFÙ�Ù@�MßTÝ'=@ÝO:\=�=@ÝJ?|;>?�Ù>�JEG=@Ù�Ø�ܹ?�A':·×�CGLJ?1:<;>;K:�ÖÈØ â :<ÜJÜJEGCFß�:\=KCGØ�AJÙCFA'ܹØ�;>= â Ø�EFCGØ�=KÝJ?IØ�;>Ö":<AJL"èOAO:<AMß�CÑ:\EÏ:<AJL'Ù>=@ØVßTÝO:\Ù>=KCGßgà3:<ßI;@Ø}?�ßIØ�AJØ�àÈCFß0àÈØ}LJ?�EGÙ�ã� AJ?$Ø â =@ÝJ?ÉèO;>Ù>=g=KÝJ?IØ�;@?7=KCGß�:<EkÙt=K�JLMCF?�ÙgØ â :"àÉ�JEh=KChÛÐÜ ?I;@CGØVL�ß�Ø�AMÙ@�JàÈÜM=KCGØ�AVÛÐCFAeá�?IÙ>=KàÈ?�Ae=6ÜJ;>Ø�HJEF?Ià�JAJLJ?I;R�MAJß�?I;>=T:\CFAe=�ÖÈLO:\=K?IÙRHJ:<ß�� =KØ��,ÝM?�EFÜMÙ �Yê_ì"!$#"%ãkBÆ?DÙt=K�JLJCG?�ÙR:6à��JEG=@ChÛ�ܹ?�;>CFØ}LÉ?'&Vܹ?�ß7=K?�L"�V=KCFEoÛCG=�Ö àË:(&VCFàÈCF��:\=KCGØ�A�ÜM;@Ø�HJEG?�à ×�Ch=KÝË:6Ù>CFAJ�<EF?�;@CGÙ)�eÖÈ:<Ù>Ù@?I=�×�ÝJ?I;@?Æ;@?I=@�J;@AMÙ â Ø�EGEFØ_× :<AËC�ã{C�ã{Lyã�ÜJ;>ØVßI?�Ù>Ù×�CG=@Ý :�LJCFÙ>ß�;>?I=K?3ÜJ;@Ø�HJ:<HJCFEGCG=�Ö#LJCGÙ>=@;@CFHM�M=KCGØ�A§ã*��ÝM?"CFAeá�?IÙ>=KØ<; CFÙ�?IAJLJØ_×R?�L ×�CG=KÝ«:<LJLJCh=KCGá<?3Ù>?�ÜO:ÊÛ;K:<HMEF?1ÜJ;>? â ?�;>?�AJßI?�ÙDØdá<?�;ÆEFC â ?I=KCGàË?Dß�Ø�AMÙ@�JàÈÜM=KCGØ�A�:<AJL';@?Iß�?ICGá�?IÙ0: ß�Ø<AJÙ>=K:<Ae=|AJØ<AVÛ�ß�:<ÜJCG=K:<EyCGAJß�Ø<àË?Ù>=@;@?�:\à)CFA�?�:<ßTÝ#ܹ?�;@CGØVLyã|� CG=@ÝJCFA�=KÝJCGÙ0Ù@?7=@=KCGAJ�":+;>?�ß��M;@Ù@Chá�? Ù>Ø�EF�M=@CFØ�A�=K?IßTÝJAJC,+r�J?$CGÙ0:<ÜJÜMEFCF?IL�=KØLJ?�;>CGá<?1Ø�ÜM=KCGà3:\EOß�Ø�AJÙ>�JàÈÜM=KCGØ�A':<AJL+CGAeá�?�Ùt=KàÈ?�Ae=�CFA3?�:<ßTÝ'ܹ?�;@CGØVLyã���ÝJ?0Ù>?I=@=@CFAJ� ßIØ_á�?�;>Ù�=KÝJ?|ß�:<Ù>?×�CG=@Ý�:ÉèOAMCG=K?g:\AJL�:\A�CGAMèOAJCh=K?1ÜJEF:<AJAJCGAJ� ÝJØ�;>CF�IØ�A':<ÙÆ: EFCFàÈCG=@CFAJ�6ß�:\Ù@?<ãRæqEGØ�Ù@?IL â Ø�;>à Ù>Ø�EF�M=@CFØ�AMÙ�ÞÝJØ_×q?7á�?I;�Þ :<;@?gØ�AJEhÖ+LJ?I;@Chá�?�L�CFA"=@ÝJ?6:<HJÙ@?IAJß�?6Ø â AJØ�AVÛÐß�:<ÜMCG=T:\E§CFAJßIØ�àÈ?<ã- A�?.&V=@?�AJÙ>CFØ�A�=@Ø+=KÝJ?�ß�:<Ù>?�×�CG=@Ý�Ü Ø<Ù@Ù@CGHJEGÖ�AJØ<AVÛY:<LMLJCG=@CGá�?·ÜJ;@? â ?�;>?�AJßI?�Ù6:<AJL�àÈØ�;>?���?IAJ?�;@:<Ek:<AMLàÉ�JEh=KCGá\:<;>CÑ:\=@? ;@?7=K�J;>A«LJCFÙt=K;>CFHJ�M=@CFØ�AMÙ6CGÙ·ÜM;@Ø_á}CFLJ?IL«CFA0/¹:\à3:1�tê_ì"243MÞ�ê_ì$24!$% ã65Æ=@CFEFCG��CGAJ��:�Ù@CGàËCoÛEÑ:<;1àÈ?I=@ÝJØ}LJØ�EFØ<�<Ö�=@ÝJ?ÈÜJ;@Ø�HMEF?�à)CFÙ1Ù@Ø<EGá�?IL ;>?�ß��M;@Ù@Chá�?IEGÖ�=KØ�Ø�HM=K:<CFA#Ø�ÜV=KCFàË:<E�LJ?�ßICFÙ@CGØ�AJÙ6:\=g?�:<ßTÝÙ>=K:<��?+Ø â =@ÝJ?+ÜJEF:<AJAJCGAJ��ÝJØ�;>CF�IØ�A§ã - Eh=KÝJØ<�J��Ý«Ch=ÉCFÙ�:<;@�<�J?�Lç=KÝJ:\= :\=É?�:<ßTÝ Ù>=K:<��?3=@ÝJ?"ÜJ;>Ø�HJEF?IàCFÙÆ×q?IEFEhÛÐLJ?IèJAJ?�L�:\AJL�CFàÈÜJEGCF?�Ù�?.&VCFÙ>=@?�AJßI?$:<AJL��MAJC,+r�J?IAJ?�Ù>Ù1Ø â :ËÙ>Ø�EF�M=@CFØ�AyÞ¹Ù>?Iá<?�;K:\E%=K?IßTÝJAJCFß�:<E%;>?7Û+r�JCF;>?�àÈ?�Ae=KÙËEFC,�\?'àË?�:<Ù@�J;@:<HJCGEFCG=�Ö«:<AJL87ÊØ�;ËCGAe=K?��<;K:<HJCGEFCh=�Ö«:<Ù$×R?�EFED:<ÙÈ?'&VCFÙt=K?IAJß�?�Ø â ß�Ø<AJLJCG=@CFØ�AJ:<ELJCFÙt=K;>CFHJ�M=@CFØ�AMÙÈAM?�?�LM?�L â Ø�;$=KÝM?�Ù>Ø�EF�M=@CFØ�A =KØ H¹?�×R?�EGEhÛ�LM?IèOAJ?IL :<;>?�AM?���EG?�ßI=@?�L =@ÝJ?�;>?<ã:9Æ?�CG=@ÝJ?�;ß�;>?�LJCh=�AJØ<;6Ù@: â ?ÈCFAeá�?IÙ>=KàÈ?�Ae=�CFÙgÜ Ø<Ù@Ù@CGHJEF?$CGA =@ÝJCFÙgÙ@?7=@=@CFAJ��AJØ�;gLJØ}?�Ùg=KÝJ?ÈCFAeá�?IÙ>=@Ø�;�;>?�ß�?ICGá<?+:<AeÖAJØ�AVÛÐß�:<ÜMCG=T:\E§CFAJßIØ�àÈ?<ã- AJØ\=KÝJ?I;0?'&}=K?IAJÙ@CGØ�A�CGAr=@Ø":ËÙ>Ø�àÈ?I×�ÝO:\=0LJC�� ?�;>?�Ae=0LJCG;@?IßI=KCGØ�A�àË:�Ö�H ? â Ø��JAJL�CGA�=@ÝJ?É:<;t=KCGß�EF?IÙDHeÖB|:4�Ê:<AMÙ@Ù@Ø<A;�tê�ì"!�ìMÞ�ê_ì"243$%·ÞÏÙ@?I?3:\EFÙ@Ø<�AJ�<?�;@Ù>Ø�EFE=�tê_ì">"2"% â Ø�;g:'Ù@�J;tá�?IÖ<ã?��ÝJ?IÙ@?ÈÙ>=@�JLJCF?IÙg;@?�Ùt=K;>CFßI=:\=@=@?�Ae=KCGØ�AË=@Ø�:6ÜO:<;t=KCFßI�JEÑ:\;�ßIEÑ:<Ù>ÙRØ â �M=@CFEFCh=�Ö â �JAMßI=KCGØ�AJÙq:<AJL3?.&}=K?�AML3=KÝJ?Æ×qØ<;)�$HeÖ?��ÝJ?IEFÜJÙ@�tê�ì"!$#"%HeÖ3:\EFEFØ_×�CGAJ� â Ø�;,ß�;@?ILJCG=�ÞM:6;@CGÙ)��Û�EG?�Ù@Ù�CFAeá<?�Ù>=@àË?IAe=�ܹØ�Ù@Ù>CFHJCGEFCG=�ÖÉ:<AJL3:<A+:<;>HJCG=@;K:<;tÖ6�vܹØ�Ù>Ù@CFHMEGÖÉ=@CFàÈ?7Ûá\:<;>Ö}CFAM�A%�Ar�JàÉH¹?�;�Ø â ;@CFÙB�eÖ":<Ù>Ù@?I=@Ù�ã�CRÖ+:<LJØ�ÜM=@CFAJ�6=KÝJ?1Ù@:<àÈ?0;@?Iß��J;>Ù@CGá<?1Ù@Ø�EG�M=KCGØ�A3=@?�ßTÝJAJC�+r�J?0=KÝJ?ß�EF:<Ù@Ù$Ø â �M=KCGEFCG=�Ö â �JAJß7=KCGØ�AJÙÈ�JAJLJ?I;ËÙ>ß�;@�V=KCFAeÖ EG?�:<Lç=KØ ß�EGØ�Ù@?IL â Ø<;@à Ù>Ø�EF�M=@CFØ�AMÙÉ×�ÝJCFßTÝ :<EFEGØd× =KØØ�HM=K:<CFAçÙ>?Iá�?I;K:<E�CGAJÙ@CG��Ýe=KÙÉCGAr=@Ø�=KÝJ?'ßIØ�AJÙ@�MàËÜM=@CFØ�A}Û�CFAeá<?�Ù>=@àË?IAe=$H ?IÝO:�áVCGØ�; â Ø�;É=@ÝJ?"ß�:\Ù@?"×�CG=@Ý :èOAJCh=K?g:<AJL�:<A�CFAMèJAJCG=@?0ÜJEÑ:\AJAJCFAM� ÝJØ�;@CG��Ø�Ayã� AJ?�Ø â =KÝM?�àË:D�>Ø�;$LJ;@:�×�HO:<ß��rÙ3ßIØ�àËàÈØ�Aç=KØ�:<EGEq=KÝJ?IÙ@?�:<ÜJÜJ;>Øe:<ßTÝJ?IÙËCGÙ$=@ÝO:\=$=KÝM?��JAMLJ?�;>EGÖ}CFAJ�LJ?�ßICFÙ>CFØ�A�ÜJ;>Ø�HJEG?�à/CFÙ1Ø�AJEhÖ â Ø<;@àÉ�JEF:\=K?IL�CFàÈÜJEGCFß�Ch=KEhÖ+CFA#:+;>?�ßI�J;@Ù>CGá�? â :<Ù>ÝJCFØ<A§ãE�r=T:<;t=KCFAM�+Ø�AJ? ܹ?7Û;@CGØVL�ÜJ;>CFØ�;0=@Ø"=KÝJ?É=@?�;@àÈCFAJ:<E%ܹ?�;>CFØ}L�:"Ù>?�+r�J?�AMß�?3Ø â Ø�AM?7Û�ܹ?�;>CFØ}L�LJ?�ßICFÙ>CFØ�A#ÜJ;>Ø�HJEF?IàËÙ1CGÙ1Ù@Ø�Ehá�?IL=KØÉØ<HM=T:<CGA+Ù@Ø<EF�M=@CFØ�AJÙ â Ø�;R?�:<ßTÝ"ܹ?�;>CFØ}L3Ø â =@ÝJ?0ÜJEF:<AJAJCGAJ��ÝJØ<;@CF�IØ�A§ã�<Ð=qCFÙ�=KÝJ?IA':<;@���M?�L+=KÝJ:\=q=@ÝJ?�Ù>?;@?Iß��J;>Ù@CGá<?�EhÖ�LJ?7èOAJ?�L LJ?Iß�CFÙ>CFØ�AMÙ0LJ?IèJAJ?$:<A�Ø�ÜM=@CFàË:<EÏÙ>=@;K:\=@?��<Ö�Ødá<?�;0=@ÝJ? ?�Ae=KCG;@?ÉEGC â ?·ßIÖ}ß�EG?<ãF��ÝJCFÙ=�Ö}Ü ?ÆØ â :\ÜJÜJ;@Ø�:<ßTÝËLMØV?IÙRAJØ\= â Ø<;@àÉ�JEF:\=K?R=KÝJ?Æ�JAJLJ?I;@EhÖVCGAJ�gØ�AJ?Û�Ù@ÝMØ<=�LJ?�ßICFÙ@CGØ�AÈÜJ;@Ø�HMEF?�à CFAeá�Ø�Ehá}CFAJ�

ê

Page 3: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

=KÝJ?ÆßTÝJØ�CGß�?ÆØ â :gß�Ø<AJÙ@�JàÈÜM=@CFØ�AVÛÐCFAeá�?IÙ>=@àË?IAr=RÙ>=@;K:\=@?��<Ö$LM;K:�×�A â ;>Ø�à�:gÙ@�JCh=T:<HJEhÖ LJ?7èOAJ?�L3Ù>=K;@:\=K?I�<ÖÙ@ÜO:\ß�?<ã - Ù6:'ßIØ�AJÙ>?�+r�J?�AMß�?<Þ%:"ß�Ø�àÈÜO:<;>CFÙ@Ø<A�×�CG=KÝ#Ùt=K;K:Ê=K?��<CF?�Ù0×�ÝMCFßTÝ LJ?Iá}CÑ:Ê=K? â ;@Ø<à =KÝM?ÈܹØ<=@?�AVÛ=KCF:<EFEhÖ0Ø�ÜM=@CFàË:<EeØ�AJ?�CFÙcAJØ<=�ܹØ�Ù@Ù>CFHJEG?RCGA·=KÝMCFÙcÙ@?I=>=KCGAJ�JãÏ� ÝJCFEG?�=@ÝJ?q;>?�ß��M;@Ù@Chá�? â Ø�;@àÉ�MEÑ:\=@CFØ�AgÙ@Ø<EF�M=@CFØ�A=K?IßTÝJAJC,+r�J?ÆCFÙ �>�JÙt=KChèO?�LÈHeÖ Ù>=@ØVßTÝO:\Ù>=KCGß�LMÖ}AO:<àÈCFß�ÜJ;>Ø���;K:\àËàÈCFAJ�0:<AJL$=KÝJ?�;@?IAJØ_×�AJ?�L3ÜJ;@CGAJß�CGÜJEF?�Ø âØ�ÜM=@CFàË:<EFCh=�ÖgLJ�J?�=KØ Cq?IEFEFàË:<A�Yê_ì$#"24%7Þ<=@ÝJ?�ÜJ;@?IÙ@ß�;>CFH¹?�LÈÙ@?7=@=KCGAJ�gLJØ}?�Ù,AJØ<=,Ø4� ?�;k=@ÝJ?�Ü Ø<Ù@Ù@CGHJCFEGCG=�Ög=KØá�?I;@C â Ö =@ÝJ?�á<:\EFCFLMCG=�Ö·Ø â =@ÝJCFÙ,ÜJ;>CFAJßICFÜJEG?�Ù@CFAMß�?ÆAJØÉ:<ÜMÜJ;@Ø�ÜM;@CÑ:Ê=K?�Ù>=@;K:\=@?��<Ö$Ù>ÜO:<ßI?|ÝO:<Ù�H¹?�?�AËLJ?IèJAJ?�L§ã- àËØ�;>?���?�AM?�;K:\E0=K;@?�:\=KàÈ?�Ae=�Ø â LJ?�ßICFÙ>CFØ�A ÜJ;>Ø�HJEF?IàËÙ"�MAJLJ?�;'�JAMß�?�;t=T:<CGAe=�Ö à3:�ÖÍH¹? â Ø��JAJL CFAég;@:<AJLJàÈØ�Ae= � BÆCFEGLJ?�HJ;@:<AJL �tê_ì$2��A%È:\AJL é1;K:<AJLMàËØ�Ae= �tê_ì4>��"%7ã ��ÝJ?IÙ@?�Ù>=@�JLJCG?�Ù3;>?�Ùt=K;@CGßI=+:\=>Û=K?IAr=@CFØ�A =KØ�:�=KÝM;@?�?Û�ܹ?�;>CFØ}L�ÜJEF:<AJAJCGAJ�'ÝJØ�;>CF��Ø<A«:<AJL�LJ?�;>CGá<?3Ù@���ËßICF?IAr=�ß�Ø�AMLJCG=@CFØ�AJÙ â Ø�;g=KÝM?Ë?.&}ÛCFÙt=K?�AMß�?'Ø â : Ù>Ø�EF�M=@CFØ�A«=@Ø�=KÝJ?'ÜJ;>Ø�HJEF?Ià�ã0��ÝJ?'CFAe=K?IAr=@CFØ�A Ø â =KÝMCFÙ$ÜO:<ܹ?�; CGÙ AJØ<=$=KØ#àË:<CFAe=T:\CFA=KÝJ? â �JEGEa��?�AJ?I;K:<EGCG=�Ö"Ø â =KÝM?�CF;�Ù>?I=K�MÜ�HJ�M=Æ=KØÈCFAJÙt=K?�:<L�;>?�Ù>=@;@CGßI=D:\=@=@?�Ae=KCGØ�A'=KØË=@ÝJ?6ÜO:<;>=@CFßI�JEÑ:<;qß�:<Ù>?Ø â :3àÉ�MEG=KCoÛ�ܹ?�;>CFØ}L�ßIØ�AJÙ>�JàËÜV=KCFØ<AVÛ�CGArá<?�Ùt=KàÈ?�Ae=0ÜJ;>Ø�HJEG?�à/:<Ù0LJ?IÙ@ßI;@CFH¹?�L#:\H Ø_á�?\ã <�A�=KÝMCFÙ|;>?��e:\;@L§Þ×q? :<àÈ?�AMLÍ=KÝJ?�?.&MCGÙ>=@CFAJ� :<ÜMÜJ;@Øe:\ßTÝJ?�Ù'HeÖ LJ?7èOAJCFAM� ßIØ�AJÙ>�JàËÜV=KCFØ<AVÛ�CGArá<?�Ùt=KàÈ?�Ae="Ù>=@;K:\=@?���CG?�Ù':<Ù:<LO:<ÜV=K?�LËÙ>=@ØVßTÝO:\Ù>=KCGßDÜM;@Ø}ß�?�Ù>Ù@?IÙ�LJ?IèJAJ?�L+CGA =KÝJ?D:<ÜJÜJ;>Ø�ÜJ;>CÑ:\=@?ÆÙ>ÜO:<ßI?|Ø â ;K:<AJLMØ�à á\:<;@CF:<HJEG?�Ù�ã ��ÝJCFÙ=�Ö}Ü ?gØ â :<ÜJÜJ;>Øe:<ßTÝ�Ù@?I?�àÈÙ�=@Ø$H ?gß�Ø<àËàÈØ�A"Ù@?IAJÙ@?6CFA+=@ÝJ?1èOAO:<AMß�?6EFCG=@?�;@:\=K�J;>? ��Ù@?�?·ë0���È?��tê�ì�ì��"%Ø�; ��EFCFÙB�Ê: �Yê_ì�ì$24% â Ø<;�=@ÝJ?gÙ@ܹ?�ßICÑ:<EÏß�:\Ù@?6Ø â :$LJCFÙ>ß�;>?I=K?6ÜJ;>Ø�HO:<HJCGEFCh=�Ö+Ù@ÜJ:<ß�? %Æ:<AML�CFÙ�=@ÝJ?�;>? â Ø�;>?·HeÖAJØgàË?�:<AJÙkAM?I×gã - àÈØ�AJ�1Ø\=KÝJ?I;,:<LMá\:<Ae=T:<�<?�Ù�ÞeØ<�J;,:<ÜJÜJ;>Øe:<ßTÝÈ:<EGEFØ_×�Ù%�JÙ�=@Ø0á�?�;>C â Ö·=KÝJ?�á\:<EGCFLJCh=�Ö·Ø â=KÝJ?g;>?�ß��M;@Ù@Chá�?6Ù@Ø�EG�M=KCGØ�A':<ÜJÜM;@Øe:<ßTÝ�:<AJL'=KØ$ÜJ;>Ø_á�?g=KÝJ?1á\:<EFCGLJCG=�ÖËØ â =KÝJ?gÜJ;>CFAJßICFÜJEG?0Ø â Ø�ÜM=@CFàË:<EFCh=�Ö�ã- ÜJ:<;>=@CFß��MEÑ:<;���Ø�:<EOØ â =@ÝJ?ÆÜO:<ܹ?�;�CFÙ�=KØ6ßTÝO:<;@:<ßI=@?�;@CG��?Æ=KÝJ?ÆLJ?�àË:<AJL â �JAJß7=KCFØ<AJÙ,LJ?IèOAMCFAJ�6=KÝJ?ÆØ�ÜM=@ChÛà3:\EOH ?IÝO:�áVCGØ�;,CFA =KÝM?DLJ?Iß�CGÙ@CFØ<AÈܹ?�;>CFØ}L§ã�/OØ�;�=@ÝJCFÙ,ÜJ�J;>Ü Ø<Ù@?�×q?D:<LJØ�ÜV=q:gÙ@EGCF��Ýe=@EGÖÉLMC�� ?�;@?IAe=RÙ>?I=@�JÜß�Ø�àÈÜO:<;>?�Lç=KØ�=@ÝJ?'EFCG=@?�;@:\=K�J;>?3×�ÝJCGßTÝ =�Ö}ÜJCGß�:<EGEGÖ â Ø�;@àÉ�MEÑ:\=@?�ÙÉ=KÝM?"LJ?�ßICFÙ@CGØ�A ÜJ;@Ø<HJEF?Ià â Ø�; ��Chá�?IAÜJ;@CGß�?IÙ :<AJLç?.&Mܹ?�ß7=T:\=@CFØ�AMÙ â Ø�;É:<Ù>Ù@?7=$;@?I=@�J;@AMÙ�ã ��ÝJCFÙ â Ø�;@àÉ�MEÑ:\=@CFØ�A Ù@?I?�àÈÙ CFAJLJ?I?�L â :�á�Ø<;K:<HJEG?+C âØ�AJ?g;@?IÙ>=@;@CFß7=KÙ�:\=>=K?IAr=@CFØ�A"=@Ø$=@ÝJ?gLJ?�ßICFÙ>CFØ�A'ÜJ;>Ø�HJEF?Ià Ø�A"=@ÝJ?gCFAJLJChá}CFLJ�O:\EyEF?7á�?IE§CFA�: ��CGá<?�A'ܹ?�;@CGØVLØ â =KCGàË?\ã�< â ÞMÝJØ_×R?Iá<?�;�ÞO=@ÝJ?1�JEG=@CFàË:\=K?Æ��Øe:\EyCFÙ�=KØ ?IàÉH ?IL"=KÝJ?1CGAJLJCGá}CGLJ�O:<E�LJ?Iß�CFÙ>CFØ�A"ÜM;@Ø�HJEG?�à CFAe=KØ:1àËØ}LJ?�EMØ â àË:<;B�<?I=,CGAe=K?�;@:<ßI=@CFØ�A ×�ÝJ?I;@?�ÜJ;>CFß�?IÙ�:<;@?�LJ?7=K?I;@àÈCFAJ?IL â ;>Ø�à =@ÝJ?�LJ?�àË:<AJLÈH¹?�ÝO:�á}CFØ�;�Ø âCFAeá�?IÙ>=@Ø�;@ÙIÞO: â Ø�;>àÉ�JEÑ:Ê=KCFØ<AÈØ â =KÝJ?0LM?�ß�CGÙ@CGØ�A+ÜJ;>Ø�HJEF?Ià�×�CG=KÝË;@?IÙ@ܹ?�ßI=�=@ØÉEF?7á�?IE§:<Ù>Ù@?I=�ÜJ;@CGß�?�ÙR;K:\=@ÝJ?�;=KÝO:\Aç:<Ù@Ù>?I=�;@?I=@�J;@AMÙÉÙ@?I?�àÈÙ�=KØ�H ?ËLJ?�Ù>CF;K:\HJEF?\ã6< â Þ�CFA :<LJLJCh=KCFØ<A§Þc=@ÝJ?3�<Øe:<E,CFÙ·:�Ù@? +r�J?�Ae=KCF:<E â Ø�;tÛàÉ�JEF:\=KCGØ�A+Ø â =KÝJ?gàÈØVLM?�E ×�ÝMCFßTÝ�ß�:<ÜM=@�J;@?IÙÆ=@ÝJ?g�JܹLO:\=KCGAJ� ÜJ;>ØVßI?�Ù@Ù�Ø â ß�Ø<AJÙ@�JàÈ?�;>Ù�?'&Vܹ?�ß7=T:\=@CFØ�AJÙ:<H¹Ø��M=·�JAJß�?I;>=K:<CFA á<:\;@CÑ:\HJEF?IÙ�ÞcCG=6Ù@?I?�àÈÙ :<LMá\:<Ae=T:\��?�Ø��MÙ6=@Ø�ÜO:<;@:<àÈ?I=K?I;@CG��?$=KÝJ?ËLJ?�àË:<AJL�H ?IÝO:�árÛCFØ�;|CFA#?'&Vܹ?�ßI=K:\=KCGØ�AJÙ6:<Ù0×R?�EGE±ãE<�A#ÜO:<;t=KCGß��JEF:<;�Þy=@ÝJCFÙ1ß�:<ÜM=@�J;@?IÙ6=@ÝJ? Ü Ø<Ù@Ù@CGHJCFEGCG=�Ö'=KÝJ:\=gß�Ø�AMÙ@�JàÈ?�;>Ù�JܹLO:\=K?·=KÝJ?ICF;Æ?'&VÜ ?IßI=K:\=KCGØ�AJÙ1:<AML�;@?7áVCGÙ@?�=@ÝJ?�CG;DÙt=K;@:\=K?I��CF?IÙ0Ø_á�?�;D=KCFàÈ?·:<Ù|AJ?7× :<AJL��JAM?'&VÜ ?IßI=@?�LCFA â Ø<;@àË:\=KCGØ�A H ?Iß�Ø�àÈ?0:�á\:<CGEÑ:<HJEG?F�vÙ>?�?1BÆCFEGEF?�HM;K:<AJL � ��?�AJ�I?�EGHJ�J;@�<?�; ���43"3"!"% â Ø�;R:·Ùt=K�JLVÖËCGAË=@ÝJCFÙÙ@ÜJCG;@Ch=.%7ã��ÝJ?+ÜO:\Ü ?I;·CGÙ·Ø�;>�e:<AJCG��?IL«:<Ù â Ø�EFEGØd×�ÙIã6�V?�ß7=KCGØ�AÍê3CGAe=K;@Ø}LJ�JßI?�Ù6=KÝJ?Ë��?�AJ?I;K:<E�Ù@?7=K�JÜçØ â :�àÉ�MEG=KCoÛÜ ?I;@CGØVLÈß�Ø�AMÙ@�JàÈÜM=KCGØ�A3CGAeá�?�Ùt=KàÈ?�Ae=�ÜM;@Ø�HJEG?�à â Ø�EGEFØ_×q?ILËHeÖË: â Ø<;@àÉ�JEF:\=KCGØ�A$Ø â =@ÝJ?|LM?�ß�CGÙ@CGØ�A3ÜJ;>Ø�HVÛEF?Ià CGA �V?�ß7=KCGØ�A��Vã ä &MCGÙ>=@?�AJßI?':<AJLçÜJ;>Ø�Ü ?I;>=@CF?�Ù�Ø â Ù@Ø�EG�M=KCGØ�AJÙÉ:\AJLçØ â LJ?Ià3:<AML â �JAJßI=@CFØ�AMÙ :<;@?Ù>=@�JLJCF?ILË�MAJLJ?�;��<?�AJ?I;K:<E�:<Ù>Ù@�JàÈÜM=@CFØ�AJÙ�CGA��V?�ß7=KCGØ�A� 6:\AJL â Ø�;%=KÝM?Æà��JßTÝVÛ�Ùt=K�JLMCF?�L$ßIEÑ:<Ù>Ù�Ø â æ -�� -ÜJ;@? â ?�;>?�AJßI?�Ù�CFA��V?�ß7=KCGØ�A��Jã��V?�ß7=KCFØ<A#6ßIØ�AJß�EG�JLJ?IÙ�Þ à3:\=@ÝJ?�àË:\=@CFß�:\E¹ÜM;@Ø}Ø â Ùq:\AJL3=K?IßTÝJAJCGß�:<E¹ÜJ;@?I;@? +eÛ�JCFÙ>CG=@?�Ù�:<;>?6ÜMEÑ:<ßI?�L'CFA - ÜMÜ ?IAJLJCFßI?�Ù - :<AJL6C|ã

Page 4: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

� � �������� �*��� � � � ��� � ����� ��� � � � ���������������

æqØ�AJÙ>CFLJ?I;�:�ß�Ø�AMÙ@�JàÈ?�;�×�ÝJØÉ=K:4�<?IÙ�LJ?�ßICFÙ@CGØ�AJÙ�CGA+LJCGÙ@ß�;>?I=@?0=KCFàÈ?<ã%åa?I=���� 3ÉLJ?�AMØ<=K?0=@ÝJ?0ß��M;@;@?IAe=Ü ?I;@CGØVL :<AJL�� � 3�=KÝJ?Ëß�Ø�AJÙ>�JàÈ?�; ÙÉÜJEF:<AJAJCGAJ��ÝJØ�;@CG��Ø�A :\=6=KÝJ?+?IAJL«Ø â ×�ÝJCFßTÝçÝJ?ËLJCF?IÙ�Ù>�JßTÝ=KÝO:Ê=Ë=@ÝJ?�Ù>?I=��(3���ê�������� �!�#"#LJ?IèJAJ?�Ù3=@ÝJ?�ßIØ�AJÙ>�JàË?I; Ù+;@?Ià3:\CFAJCGAJ�#EFC â ?7=KCGàË?\ã <�AÍ?�:<ßTÝÍܹ?�;@CGØVL$ % �(3���ê��������&�!�#"�=@ÝJ?�ß�Ø�AMÙ@�JàÈ?�;";>?�ß�?ICGá<?�Ù�:«AJØ�AVÛÐß�:<ÜJCh=T:<EDCFAJßIØ�àÈ?�'�(*) 3Mã �cØ =@;K:<AMÙ â ?�;CFAJßIØ�àÈ?ÆH¹?I=�×R?�?IA+LJC �y?I;@?�Ae=RÜ ?I;@CGØVLJÙ�=@ÝJ?�;>?|:<;>?,+.- ê�CFAeá�?IÙ>=KàÈ?�Ae=qÜ Ø�Ù>Ù@CGHJCFEGCG=KCG?�Ù�ß�Ø�;>;@?�Ù>Ü Ø<AJLJCFAM�=KØ�LJC�� ?�;>?�Ae=Ë:<Ù@Ù>?I=KÙ0/ � 3���ê��������&� + CGA ?�:<ßTÝÍܹ?�;@CGØVLyã ��ÝJ?'èO;@Ùt=+:\Ù@Ù@?7=�/ � 3#CFÙÈ:�Ø<AJ?7ÛÜ ?I;@CGØVL"EGCGá�?IL'H Ø�AML'×�ÝMCFßTÝ�CFÙ�=K;@:<LJ?IL�:\=Æ: ÜJ;>CFßI?1Ø â �MAJCG=�Ö+:\=�=KCGàË? $ :<AML�ÜJ:_Ö}ÙD: AJØ�AVÛÐ;K:<AJLMØ�à;@?7=K�J;>A21,(�� 3�CFA =@ÝJ? â Ø�EFEGØ_×�CFAJ��Ü ?I;@CGØVL $ -�ê�ã �VCFAMß�?31,(�CFÙ·LJ?I=@?�;@àÈCFAM?�L :\=·=KCFàÈ? $ Þk=KÝJ?H Ø<AJL ÜM;@Ø_á}CFLJ?IÙ3:#;@CGÙ)�rEF?IÙ@ÙÈCFAeá�?IÙ>=KàÈ?�Ae=ËÜ Ø<Ù@Ù@CGHJCFEGCG=�Ö H ?7=�×q?I?�A :<AeÖç=�×RØ ßIØ�AJÙ@?Iß��M=@CGá<?�ܹ?�;@CGØVLMÙ�ã��ÝJ?�;>?�àË:<CFAMCFAJ�$:<Ù>Ù@?7=KÙ�/4�Çê��������5�!+ :<;@?g;>?I=K;@:<LJ?�:<HJEF?6Ù@ÝJ:<;@?IÙD×�ÝJCGßTÝ�:<;@?1=@;K:<LJ?IL�:\=ÆÙ>=@;@CGßI=KEhÖÜ Ø<Ù@CG=@CGá<?�:\Ù@Ù@?7=�ÜM;@CFßI?�Ù768(9� �:6<;>=@?( �������5�A6<;CB�?( %ED % F BGHG :<AML ÜO:�Ö : AJØ�AVÛÐAJ?���:\=KChá�?#;K:<AMLJØ�àLJCGá}CGLJ?�AJLJI�(J� �KI8;>=@?( �������5�!I�;LB�?( %MD %NF BG ��ÜJ;@CGØ�;§=KØ�=K;@:<LJCFAM�A%§CFAg?�:<ßTÝ�Ü ?I;@CFØ}L $#% �(3���ê��������&�!�O"rã��ÝJ?+H¹Ø�AJL�à3:�Ö#H¹?3Ù@Ø<EFL Ù>ÝJØ�;t=�×�CG=@ÝJØ��M=·H¹Ø��JAJL«HM�M=ÉAJØ�Ù@ÝJØ<;>=ÉÙ>?�EGEFCFAM��Ø â Ù@ÝO:\;@?�Ù�CFÙ6Ü Ø�Ù>Ù@CGHJEF?Ù@�JßTÝ�=@ÝO:\=D=KÝJ?·Ù@?I=@Ù,PQ� F :<AJLNR*� F BG LM?�Ù@ßI;@CGH ? â ?�:<Ù@CGHJEF?gH¹Ø�AJL�CGAeá�?�Ùt=KàÈ?�Ae=KÙ|;@?�Ù>Ü ?IßI=@CGá�?IEGÖâ ?�:<Ù>CFHJEG?|;>CFÙ)�eÖËÜ Ø<;>= â Ø<EFCFØ<Ù�CGA+?�:\ßTÝ�ܹ?�;>CFØ}L§ã���ÝJ?1Ù>ÜO:<ßI?�SÍÚT�UPUV�R LJ?7èOAJ?�Ù�=@ÝJ?1Ù@?7=�Ø âaâ ?�:<Ù@CGHJEF?Ü Ø<;>= â Ø<EFCFØ<ÙqCFA'?�:<ßTÝ�ܹ?�;>CFØ}L§ãë0?�AJØ\=K?+HeÖXWZY = � �K[\Y = �^]_Y = % % S�=KÝJ?+ܹØ�;t= â Ø�EGCFØ'ÜJ�J;>ßTÝO:<Ù@?IL HeÖ =KÝJ?3ß�Ø�AJÙ>�JàÈ?�;ÉLJ�M;@CFAM��=KÝJ?ÜJ;@?7á}CFØ��JÙÈܹ?�;@CGØVL ß�Ø<AJÙ@CGÙ>=KCGAJ� Ø â :#H Ø�AML CFAeá<?�Ù>=@àË?IAe=�[`Y = % P/:<AJLÍ: AJØ�AVÛÐAJ?���:\=KChá�?"á�?IßI=KØ<;]_Y = % R LJ?7èOAJCFAM��=KÝJ?ËAr�JàÉH¹?�;ÉØ â Ù@ÝO:<;>?�ÙÉCGA =KÝM?3ܹØ�;>= â Ø�EFCGØJã ��ÝJ?+CGArá<?�Ùt=KØ�; {ÙÉCGAJCG=@CÑ:<E�×q?�:<EG=@Ý:\=|=@CFàÈ?J��� 33ß�Ø<AJÙ@CGÙ>=KÙ|Ø â ÝJCFÙDß��J;>;@?�Ae=gAJØ<AVÛ�ß�:<ÜJCG=K:<EÏCFAJßIØ�àÈ?a'�bc) 33:<AJL�ÝJCGÙ0ß�:<ÜMCG=T:\EcCGAJß�Ø<àË?ß�Ø�;>;@?IÙ@ܹØ�AJLJCGAJ�3=KØÈ=KÝJ?·;@?7=K�J;>A�Ø�A�ÝMCFÙ|ÜM;@?Iá}CGØ��JÙ|CGAeá�?�Ùt=KàÈ?�Ae=�WZY = ß�Ø�AJÙ>CFÙt=KCFAM�3Ø â =@ÝJ?�;>?I=@�J;@A�Ø<A=KÝJ?�H¹Ø�AJL$CGArá<?�Ùt=KàÈ?�Ae=@��×�ÝJCGßTÝÈCGÙkAJ?I�e:\=KChá�?�C â [`Y =ed 3$%%:<AML$=@ÝJ?�LJCháVCGLJ?�AML ?�:<;>AJCFAJ�<Ù,:<AJL Ù@?IEFEGCFAJ�;@?7á�?�Ar�J?·Ø â =KÝJ?gÙ>=@ØVß��"CGAeá�?�Ùt=KàÈ?�Ae= ��×�ÝJCGßTÝ�CGÙ�Ü Ø�Ù>CG=@CGá�? %7ã%��?1=KÝJ?I;@? â Ø�;@?6Ù@?7=

f bDÚT�g'�b�-h[\Y =�i 1jY = -�] D Y = �:6Hb�-kIlb.% �têD%â Ø�;$=KÝJ?�ß�Ø�AJÙ>�JàÈ?�; Ù+CGAJCG=@CÑ:<E�×q?�:<EG=@ݧã <Ð=ËCFÙË:<Ù>Ù@�JàÈ?�LÍ=@ÝO:\=È=KÝJ?�LJ?�ßICFÙ@CGØ�A CGAk�3� 3�CGÙËàË:<LJ?mMn oqp&r =KÝM?+LJCGá}CGLJ?�AJL ÜO:�ÖVàÈ?�Ae=Ilb %sF BG :<AML =KÝJ?3ß�Ø�AJÙ>�JàÈ?�; Ù ß��M;@;@?IAe= AJØ�AVÛÐß�:<ÜMCG=T:\E�CGAJß�Ø<àË?'�bt) 3�ÝO:�á<?"H ?I?�AçØ�HJÙ>?�;tá�?�L HJ�M=vu r wAxyr =@Ø�=K;@:<LJCFAM�JÞkC±ã ?<ãhÞkH¹? â Ø�;>?Ë=@ÝJ?+H¹Ø�AJL«;>?I=K�M;@A21zb$:<AML:<Ù@Ù>?I=3ÜJ;@CGß�?�Ùj6Hb+ÝJ:_á<?�H¹?�?IAÍLJ?I=@?�;>àËCGAJ?�L§ã BÆ?�AJßI?�=@ÝJ?�ßIØ�AJÙ>�JàË?I;Ë=@;@?�:Ê=KÙ$=KÝJ?IÙ@?�á\:<;>CÑ:<HMEF?�ÙÈ:<ÙÜO:<;@:<àË?7=K?I;@Ùa1{� 3�:<AJLN6 %|F BGHG ã�åaC,�\?I×�CFÙ>?3ÝJCGÙ·ßI�J;@;>?�Ae=É×R?�:<Eh=KݫܹØ�Ù>CG=KCGØ�A#LJ?IèJAJ?�LçHeÖ �têD%CFÙÆ=K;@?�:\=K?IL#:<Ù0ÜO:\;K:<àÈ?I=@?�; f}%~F CFA�=KÝJ?ÉLM?�ß�CGÙ@CGØ�A�ÜJ;>Ø�HJEF?Ià�ã - Eh=KÝJØ��M��Ý�=KÝM?ÉEÑ:\=>=K?I;Dá\:<EF�M?·×�CFEGE��?�AM?�;@CGß�:<EGEGÖ���×�ÝJ?IAJ?Iá<?�;�]_Y =v�� 3$%�LJ?IÜ ?IAJL�Ø�A�ß��J;>;@?�Ae=0:<Ù@Ù>?I=DÜJ;@CGß�?�ÙIÞ Ch=�×�CFEFEyH ?6ß�Ø�Aeá<?�AJCG?�Ae=0=KØ=K;>?�:\=Æß��M;@;@?IAe=Æ×R?�:\EG=KÝ�:<ÙÆ: Ù@?IÜO:<;K:Ê=K?gÜO:<;@:<àË?7=K?I;�ã- =·=@CFàÈ?7�v� 3'=@ÝJ?3ßIØ�AJÙ>�JàË?I;·ÝMØ�EFLJÙ6?'&Vܹ?�ß7=T:\=@CFØ�AJÙ��'�ÚT� ���' = ���������l�'�� % %|F �G â Ø�;gÝJCGÙ â �M=@�J;@?AJØ�AVÛÐß�:<ÜMCG=T:\E§CFAJßIØ�àÈ?0×�CG=KÝ��'�(�) 3ÈLM?�AJØ<=@CFAJ� =@ÝJ?·AMØ�AVÛ�ß�:<ÜJCh=T:<E CFAJßIØ�àË?1?.&VÜ ?IßI=K?IL�=KØÈ;@?Iß�?ICGá�?6CFAÜ ?I;@CGØVL $O% �rê��������5�!�O"rã,åaC��<?I×�CGÙ@?DÝJ?0ÝJØ�EGLJÙq?.&VÜ ?IßI=T:Ê=KCFØ<AJÙ �1 ÚT� � �1 = ��������� �1���Y = % %NF ��Y =GHG â Ø�;â �M=K�M;@?qH¹Ø�AJL�;@?I=@�J;@AMÙ%×�ÝJ?�;>? �1,(DCFÙcÝJCFÙ�Ü Ø�CGAe= â Ø�;>?�ß�:<Ù>= â Ø�;�=@ÝJ?qH¹Ø�AJLÉ;>?I=@�J;@A�1,(DH¹?I=�×R?�?�A â �M=@�J;@?Ü ?I;@CGØVLJÙ $ :\AJL $ - ê�Þ $�% �rê�������������� ê�"rã /OØ�;�=KÝJ? â Ø�EFEGØd×�CGAJ�$LJ?�;>CGá\:\=@CFØ�AJÙ�=@ÝJ?�ßIØ�AJÙ@�MàË?I; ÙÜJEÑ:\AJAJCFAM�DÝJØ<;@CF�IØ�A7� :<Ù�×R?�EGEM:<Ù�ÝJCFÙ�?'&Vܹ?�ßI=K:\=KCGØ�AJÙc×�CFEFErH¹?�:<Ù>Ù@�JàÈ?�L·=KØ0H¹?Rè &V?IL +}�J:<Ae=KCG=@CF?IÙ%:<AML

Page 5: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

×�CFEGE =KÝM?�;@? â Ø�;@?6H¹?1Ù@�JÜJÜM;@?�Ù>Ù@?IL#:<Ù�:<;@�<�JàË?IAe=KÙ�Ø âcâ �JAJßI=@CFØ�AMÙ�ÞO?I=@ß<ã�=KØÈ:<EGEF?7áVCF:\=K?D=KÝJ?gAJØ<=K:\=KCGØ�A§ã<�AÍ?�:\ßTÝÍÜ ?I;@CGØVL $ % �(3 ��ê��������5�!�#"�=KÝM?�ß�Ø<AJÙ@�JàÈ?�;Ëß�:<A ß�Ø�AJÙ>�JàÈ?�ÜO:<;t=3Ø â ÝJCFÙÈ×q?�:<EG=@ÝÍ:<AML�JÙ@?É=@ÝJ?�CGAeá�?�Ùt=KàÈ?�Ae=gܹØ�Ù@Ù>CFHJCGEFCG=@CF?IÙ�LJ?�Ù>ß�;@CGH ?IL :<H Ø_á<?�=KØ3=@;K:<AMÙ â ?�;D×q?�:<EG=@Ý�CFAe=KØ â �M=K�J;>?Éܹ?�;@CGØVLMÙ�ã� ?IÙ>=@;@CFß7=KCGAJ�DßIØ�AJÙ>�JàËÜV=KCFØ<A6=@Ø|H¹?RAJØ<AVÛ�AJ?I�e:\=@CGá�?,=KÝM?RÙ>?I= � � F G LJ?IèJAJ?�Ù â ?�:<Ù@CGHJEF?,ßIØ�AJÙ@�MàËÜM=@CFØ�AÜJEÑ:\AJÙ�CGA·?�:<ßTÝÉܹ?�;>CFØ}L§ã /OØ�; $ �;3ÆLJ?�AJØ\=K?R=@ÝJ?�ÜO:<CF;���($ÚT� �:6�(��!I�("% %�� Ø â ÜJ;@CGß�?�Ù%:<AJL·LJCGá}CFLM?�AJLJÙCFA�ܹ?�;>CFØ}L $ ×�ÝJ?�;>? � ÚT� F BGHG V F BG LJ?�AMØ<=K?IÙ0=KÝJ?·ß�Ø�;>;@?�Ù>Ü Ø<AJLJCFAM�+ÜJ;@CGß�?Û�LJCháVCGLJ?�AML�Ù@ÜO:\ß�?<ã@<�AÜJ;@CGAJß�CGÜJEF?\Þ =@ÝJ?Éá�?IßI=KØ<;���("ßIØ��JEGL�ß�Ø�Ae=T:\CFA�Ø<=@ÝJ?�;1�JAMß�?�;t=T:<CGA�á\:<;@CF:<HJEF?IÙ�Þ§ÝMØd×R?Iá<?�;IÞc=@ÝJ? ÜJ;@?7á}CFØ��JÙLJ?IèJAJCG=@CFØ�A+×�CGEFE�=K�J;>A�Ø<�M=�=KØ H¹?1Ù@���ÈßICF?�Ae=D:<AJL"ßIØ�Ae=T:<CGAJÙ�:<EGEy;@?IEF?7á<:\Ar= +}�J:<Ae=KCG=@CF?IÙ�=KØ â Ø�;>àÉ�JEÑ:Ê=K?:<AJL+Ù>Ø�EGá<?|=KÝM?|ß�Ø<AJÙ@�JàÈ?�; {Ù�LM?�ß�CGÙ@CGØ�A3ÜJ;>Ø�HJEG?�à�ã - =q=@CFàÈ? ��� 3·=@ÝJ?�;>?0CFÙR�JAJß�?I;>=K:<CFAe=�Ö3:<H Ø<�M=�:\EFEâ �M=K�M;@?���(VÞ $ � 3È×�ÝJCFßTÝ#:<;>?·=@;@?�:Ê=K?�L#:\Ù|;K:\AJLJØ�à á\:<;@CF:<HJEF?IÙDCGA�=@ÝJ?ÉLJ?Iß�CFÙ>CFØ�A�ÜJ;@Ø�HMEF?�à�ã|9�Ø�;@?Ù@ܹ?�ßICGèOß�:<EFEhÖ�Þ\=@ÝJ?qßIØ�AJÙ>�JàË?I;%ßIØ�AJÙ@CGLJ?�;>Ù â �M=@�J;@?RÜJ;@CGß�?�Ù%:<AJLÉLMCGá}CFLJ?IAJLJÙ%:<Ùk:<A � Û±á\:\EF�M?�L|Ùt=KØ}ßTÝO:<Ùt=KCFßÜJ;@Ø}ß�?IÙ@Ùj����( "�( = Ø â ;K:<AMLJØ�à á\:<;>CÑ:<HJEG?�Ù�LM?IèOAJ?IL�Ø�A�:ÈÜM;@Ø�HO:\HJCFEGCG=�ÖËÙ@ÜO:<ßI?������� ��� %�×�ÝJCFßTÝ�:<;@?:<LO:<ÜV=K?�L'=KØÈ:$Ù@�JCh=T:<HMEF?|èOEh=K;@:\=KCGØ�A��� ,(\"�( = Ø â Ù@�MHVÛ�� Û�:<EF�<?�HJ;@:<Ù�Ø â �ã =��ÝJ? â Ø�EFEGØd×�CGAJ�ÉAJØ\=KCFØ<A�Ø â :$Ù>=K;@:\=K?I�<Ö+×�CGEFE§H¹?g?�àÈÜJEFØ_Ö�?IL�CGA'=@ÝJ?gÙ@? +}�M?�E±ã <�A�=@ÝJCFÙ�;>?��e:<;>L§Þ�� ���=%LJ?�AMØ<=K?IÙÆ=@ÝJ? CqØ�;@?IE�� ÛR:<EG��?�HJ;@:ÉØ�A�: =@Ø�ܹØ�EFØ��<CFß�:\E Ù>ÜO:<ß�?���ã�������! #"$ #%&�(')+*-,/.1032$46587:9�;�<=*�2�4>5?<�@BAC<�DFE�G>*+5HAJI+*K58<ML � ��N&b��FN = � i % �������&�BN&�@� i %)% 082�465�*+5?<=*+4CE/2�OPARQ6D30B*K5S*�2$4N b % � A4TQ � � � ( %��U� � � % 9�DVA5?7:@FA6W�I�D�OX7:4&0$<=*#2$465 N!( Ú � ( �TY � OZ2$@[D\A�0^] $ � ê��������&�!�`_

)K*+*-,a.b4c*+4&d$DB58<=9�DB4&<e5?<�@BAC<�DFE�Gc*K5UAfI+*K58<hg � �@W�b��!W = � i %&�������&�!W��@� i %B% 082$4C5�*K58<=*+4CE>2$OiAaQ6D30B*K5S*�2$4W�be� �K[Zb��^] b'% % S A�4TQ � � � ( % �j� �KS % 9RD\A�5?7�@BA6W�I#DkOX7:4T0�<=*#2$465 W�(J� � [Z(`�^]H("%�Ú � ( �lY SOZ2$@bD\A�0^] $ � ê��������5�!�`_

)+*K*K*m,on!]TDi;�A*K@ � L � g % *+5p0VA�I+I�D3QqA ß�Ø<AJÙ@�JàÈÜM=@CFØ�A"CGArá<?�Ùt=KàÈ?�Ae=�Ù>=@;K:\=@?��<Ö 2$@r5S*K9s;lImG�A Ù>=@;K:\=@?��<ÖT_- ßIØ�AJÙ>�JàËÜV=KCFØ<AËÙt=K;K:Ê=K?��\Ö L Ù@ܹ?�ß�ChèO?�Ùq:6ßI�J;@;>?�Ae=�ßIØ�AJÙ>�JàËÜV=KCFØ<AËLJ?Iß�CGÙ@CFØ<AfN bq:\AJL3ßIØ�AJÙ@�MàËÜM=@CFØ�AÜJEÑ:\AJÙ â Ø�;�:<EGE â �M=@�J;@?1ܹ?�;>CFØ}LJÙ $ �&ê����������!�)×�Ch=KÝJCGA+=KÝJ?gßIØ�AJÙ@�MàË?I; ÙÆÜMEÑ:<AJAMCFAJ�ÉÝMØ�;@CG��Ø�A"×�ÝJCGßTÝ:<;@?,àË:<LJ?�ßIØ�AJLJCh=KCFØ<AO:<E<Ø<A6=@ÝJ?,;K:<AJLMØ�à á\:<;>CÑ:<HJEG?�Ù!� = ���������\��(�Ø<HJÙ@?I;>á�?ILÉ�JÜg=KØ�=KCGàË? $ ãut$åÏC��<?7×�CFÙ@?=KÝJ?#CGArá<?�Ùt=KàÈ?�Ae=�Ù>=K;@:\=K?I�<Ö g Ù@ܹ?�ßICGèO?IÙ�:çßI�J;@;>?�Ae=�CGAeá�?�Ùt=KàÈ?�Ae= W�b�� �K[�b��^] b'%+:<AJL ÜJEF:<AJAJ?ILCFAeá�?IÙ>=@àË?IAr=@Ù0CFA�H Ø<AJLJÙ0:\AJL�Ù@ÝJ:<;@?IÙ â Ø�;D:<EFE â �M=@�J;@?·Ü ?I;@CFØ}LJÙIã@�}CFAJßI?6=@ÝJ?Éß�Ø<AJÙ@�JàÈ?�; {ÙD?�ßIØ�AJØ�àÈCFßEFC â ?Ë?IAJLJÙ CFA Ü ?I;@CFØ}L~� Þ�AJØ�ܹØ�;>= â Ø�EFCGØ�CGÙ�ß�:\;@;@CG?�L«Ø_á<?�;É=KØ�Ü ?I;@CFØ}L~�{-&ê3Ù@�JßTÝç=KÝJ:\=�W��wv 3â Ø�;0=KÝM?ÈCGAeá�?�Ùt=KàÈ?�Ae=·ÜJEÑ:<A#CGA ܹ?�;>CFØ}LO��ã <�A =@ÝJ?$Ù@? +}�M?�E,×q?ÈÙ@ÝO:\EFE�:<LMØ�ÜM=g=KÝJ?$AJØ\=T:\=@CFØ�Ax� ( = ÚT��Z� = ���������\��("% %��

( Þ $ )µê0:<AML3Ù@?7= �1zbDÚC�U1Éã /O�J;>=@ÝJ?�;>àËØ�;>?<Þe×R?|Ù@ÝJ:<EFE â ;@? +r�J?�Ae=KEhÖÈÙ@�JÜJÜM;@?�Ù>Ù�=KÝJ?:<;@�<�JàË?IAe=KÙ|Ø â :3ÜJEÑ:\A â Ø�;DÜ ?I;@CFØ}L $ Þ ×�;>CG=KCGAJ�F�>�MÙ>=UN!(VÞ<[Z(VÞ§:\AJLN]H(+CGAJÙ>=@?�:<L�Ø â N!( �=� ( = %7Þ [Z( �Z�

(= %7Þ

y NP>-(:QJ9X(:*-,S48E�._!2>-#FzX(+4V% Q[Y�`V`8!2Q 0'Q0[>_# 0 0[>�! HZ4V*-Q[Y�?J!/% T_!2%'H/!/({z8!2QEUY10'Y�%[!A#8Q'Q[!Z0JT�%[( HZ!�Qa#8*-, ,�(|zX( ,1!/*-,-Q 0[4.�!J0[>-!)T�%[(:?)#&%'W Q 4VY�%IHZ! 4&EP%'#8*-,148?J*�!�Q[Q=#8*-, Y-*-HZ!2% 0I#&(:*V0�WU} >-(+7:!JEUY10[Y-%[!)*�4V*�~�H/#&T-(K0I#&7�(+*_HZ48?J!�Q #&*-,"._4V*-,%'!Z0'Y�%'*-Q #&%'!D!2(K0'>�!/% 9X*�4B} * 48% H2#&* ._! %'!/7 # 0'(|zV!/7:W)T�%[!�HZ( Q !27+W)T-%[!�,1(:HZ0[!�, \CNP>�( Q HZ48%'%'!2Q[T_4V*-,�Qe0[4 0[>-! Q�0I#&*-,�#8%',Q[!Z0'Y�T #&T�T-7+(:!2, (:* ?J4�Q�0 ?J41,1!/7 Q (:*M0'>�! 7+(+0[!2%'#&0[Y�%'!8\

� NP>-!$7:(K0'!/%I# 0'Y�%[!$4&E 0'!/* ,1!^�-*�!�Q #"Q�0'%'#&0[!2`8W3#8Q #&* #V,�#&T10'!2,SQ 0[41HI>-#VQ�0'(:H�T�%[41H/!2Q'Qa,1!^�-*�!�,O48* # T�%'48.-#8.�(:7+(+0�WQ[T-#VHZ!G%'!/T�%'!2Q[!/*�0'(+*�`=Y�*_HZ!/%[0'#8(+*JEUY�0[Y�%'!�Q 0'# 0'!2Q648E 0[>�!�}e4V%[7 , \�� >-(+7:!G0'>�!�,1!^�-*�(+0[(:48*)`8({z8!2*J>�!/%'!G( QC!S��Y�({z #&7:!/*�0EU%'48? #J?)# 0'>�!/?)# 0'(:H2#&7�T�48(:*�0�4&E6zX(+!S} @�0'>�! Y�*-H/!/%[0'#8(+*�0�WM>-!/%'! %[!�Q�0IQ 48* EUY10'Y�%[!a#8Q'Q !/0GT�%[( HZ!�QG#&*_, ,�(|zX( ,1!/*-,-Q%I# 0'>�!/%P0'>-#&* Q 0'#&0[!2QP48E�0'>�!�}e4V%[7 , \6NP>�( Q EU48%'?Y�7 # 0'(+4V* #8T�T�!2#&%IQ ?J48%'!=Q[Y�(+0'#8.�7+!=EU%'48? #&* !2HZ4V*�48?J( H T_4V(+*�0G4&EzX(:!^} Q (:*-H/! T-%[( HZ!�Q #&*-,A,1({zX(:,1!2*-,�Q #8%[! 0[>-! %[!27+!Sz #8*�0���Y-#8*�0[(+0[(:!2Q�} >�( HI> #&%'! ,1(:%'!2H 0'7+W$48.-Q[!/%Zz #&.�7:!8\

Page 6: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

:<AJLc]H( �Z� ( = %7ã�é1CGá<?�A�=@ÝJ?�Ù>?�ß�Ø<Ará<?�Ae=KCGØ�AJÙIÞ�=KÝJ? â Ø<EFEFØ_×�CGAJ��LJ?IèOAMCG=KCGØ�A�ßTÝJ:<;K:<ß7=K?I;@CF�I?�Ùk=@ÝJ?qÙt=K;K:Ê=K?��<CF?�Ù×�ÝJCFßTÝ�:<;>? â ?�:<Ù@CGHJEF? â ;>Ø�à =@ÝJ?gCFAJCh=KCF:<E Ù>CG=@�O:\=KCGØ�A':\=�=@CFàÈ?z��� 3Vã�������! #"$ #%&���� *Zd$DF4o<=]&DqWC2$4TQR@\D$<�7�@�4 1}� 3�� A�5�5\D$<[;T@�*�03DB5 6�� 3 A�4&QR*K46*Z<=* A�I���DVA�IZ<=] f AC< <=*+9RD � � 3�� A5?<�@BAC<�DFE�G � L � g % *K5b0\A�IKI#D8QqOZDVA5�*�WI�D *KO)+*-, N b -2[�b -2] Db 6�� f)K*+*-,aOZ2$@bD\A�0^] $ � ê��������5�!�

N!( -h[y( -2] D( 6�(J� �'�(,- �1 (ZY = [Z(yY = -�] D(ZY = �L68( -hIl("% �� ( = %�� ( _n!]TDb5VD$<r2$O�A�I+I�5?<�@BAC<�DFE *#DB5��]6*#0^]�A�@\DpOZDVA�5S*�W�I#D O�@V2$9 �@1a�A6 � f % *+5bQ6DB4T2�<XD8Q WVG

B�@1a�@6 � f %V_

��ÝJ;@Ø<�J��ÝJØ��V=�×q?1Ù>ÝO:<EFEy:<Ù@Ù>�JàÈ?0=KÝO:\=q=KÝJ?1Ùt=K;K:Ê=K?��\Ö+Ù@?7=B�@1a�@6 � f %,CFÙ�AMØ�AVÛ�?IàËÜV=�Ö�ã�æqØ�AJLMCG=KCGØ�AJÙ

�JAJLJ?I;|×�ÝJCGßTÝ�=KÝJCGÙDCGÙD=KÝM?�ß�:\Ù@? :<;>?�Ùt=T:\=@?�L�CFA�åa?�àÈà3:�êÉH ?IEFØ_×gã - Ù@Ù>ØVßICÑ:\=@?�L�×�Ch=KÝ�=@ÝJ?�ßTÝJØ<CFß�?Ø â :<A�CGAeá�?�Ùt=KàÈ?�Ae=ÆÙ>=@;K:\=@?��<Ö g CFÙ�=@ÝJ?gCFAJLM�Jß�?IL�×R?�:<Eh=KÝ�ÜJ;@Ø}ß�?IÙ@Ùj����( � g �\� ( = %!"

�(� = ×�ÝJ?I;@?��( � g �\� ( = %�ÚC� �'�( - �1,(yY = [Z(ZY = -�] D(ZY = �:68( -kI�($% � � �"%

��ÝJ?È;@?�:\E�A}�MàÉH ?I;���( � g �\� ( = %0LJ?�Ù>ß�;>CFH¹?�Ùg=KÝJ?$ß�Ø<AJÙ@�JàÈ?�; {Ù â �M=@�J;@?$×q?�:<EG=@Ý :Ê=1=KCFàÈ? $ ) ê$LJ?7ÛÜ ?IAJLJCGAJ�gØ�A =KÝJ?�CGArá<?�Ùt=KàÈ?�Ae=�Ù>=K;@:\=K?I�<Ö g � �KW�($% �(� 8b � �K[y(��M]H($% �(� 8b :<AJL =KÝM?Æ;@:<AJLJØ<à á\:<;@CF:<HJEG?�Ù� = �������&�\��(ÈØ�HJÙ@?I;>á<?�L��JÜ�=KØ3ܹ?�;>CFØ}L $ ã 9DØ<=@?6=@ÝO:\=Æ×q?�:<EG=@Ý�àË:�Ö"×q?IEFEÏH ?Iß�Ø�àÈ?6AJ?��e:Ê=KCGá<?<ã�BÆØd×�Û?Iá<?�;�Þ§=@ÝJ? â Ø<EFEFØ_×�CGAJ�3åa?IàËàË:�ê·Ù@ÝJØ_×�Ù0=KÝJ:\=|=@ÝJ?�;>?É?'&VCFÙt=1EFØ_×R?�;DH Ø��MAJLJÙ0Ø�A�ÜJEÑ:<AMAJ?�L�H¹Ø�AJL�CGAVÛá�?IÙ>=KàÈ?�Ae=@Ù�:<AJL$Ø�A =@ÝJ?�×q?�:<EG=@ÝÈÜM;@Ø}ß�?�Ù>Ù�×�ÝMCFßTÝË:<;@?�?IÙ@Ù@?IAe=KCÑ:\EFEGÖ�LJ?I=@?�;>àËCGAJ?�L$HeÖ =KÝJ?�LMCFÙ@ßIØ��JAe=K?ILAJØ�AVÛÐß�:<ÜMCG=T:\E§CFAJßIØ�àÈ?0Ù>=@;@?�:\à�ã��cØËØ<HM=T:<CGA':ÈßIØ�àÈÜO:<ßI=�AMØ<=T:\=@CFØ�A"LM?IèOAJ?g=KÝM?gá\:<EG�J?�Ù

�� b ÚC� �' = -�' t�1 =

-U������- �'���1 = i�i�i �1z��Y =

):3���( ÚC� �'�( G =�1,( -U����� - �'��

�1,( i�i�i �1���Y =):3�� $ �&�������5�!� �� $%

LJ?�;>CGá<?�L â ;>Ø�à =@ÝJ?·?.&VÜ ?IßI=T:Ê=KCFØ<AJÙ0�'É:<AJL �1&×�Ch=KÝ'=KÝJ?6�JAJLJ?I;@Ùt=T:<AJLMCFAJ�$=KÝO:Ê= �� � ÚC� 3Vã /OØ�;�?�:<ßTÝâ �M=K�M;@?0ܹ?�;>CFØ}L $ �&ê�������������ÞV=@ÝJ?|á\:<EG�J? ���(�):3�LJ?7èOAJ?IÙ�=KÝJ?0LMCFÙ@ßIØ��JAe=K?IL"AJØ�AVÛÐß�:<ÜMCG=T:\E¹CGAJß�Ø<àË?Ù>=@;@?�:\à ?'&Vܹ?�ß7=K?�L =@Øç;@?�ßI?�Chá�?#: â =@?�;+ܹ?�;>CFØ}L $ ã&åaC,�\?I×�CGÙ@?<ÞÆ��Chá�?�AÍ=@ÝJ?�ßI�J;@;>?�Ae='H Ø<AJL ;@?7=K�J;>A1 � 3MÞe=KÝJ?�á\:<EG�J?a�� b���1 LJ?IèJAJ?�Ù,=KÝJ?�?.&VÜ ?IßI=K?IL â �M=@�J;@?�AJØ<AVÛ�ß�:<ÜJCG=K:<EMCGAJß�Ø<àË?�Ùt=K;>?�:<àÇLMCFÙ@ßIØ��JAe=K?IL=KØÉ=@ÝJ?1LJ?�ßICFÙ>CFØ�A"ܹ?�;>CFØ}L0��� 3Mã 5Æ=@CFEFCG��CGAJ�6=@ÝJ?�Ù>?0á\:<EF�J?IÙ�ÞM=@ÝJ? â Ø�EGEFØ_×�CFAJ�6EF?IàËàË:·?IÙ>=K:<HJEFCGÙ@ÝJ?IÙ�=KÝJ?LJ?�Ù>CF;>?�LçÜJ;>Ø�Ü ?I;>=@CF?�Ù·Ø â =KÝM?3ß�Ø<AJÙ@�JàÈ?�; {Ù CGAeá�?�Ùt=KàÈ?�Ae= H¹?�ÝO:�á}CFØ<;É:<AJL�=KÝJ?3×R?�:\EG=KÝ ÜJ;@Ø}ß�?IÙ@Ù :<AMLÜJ;@Ø_á}CFLM?�Ù�ß�Ø�AMLJCG=@CFØ�AJÙ��MAJLJ?�;�×�ÝJCGßTÝ�=@ÝJ?gÙ>=K;@:\=K?I�<Ö"Ù>?I=ÆCFÙ�AJØ<AVÛ�?IàËÜM=�Ö<ã�M������� '� D$< �� b�) 3 A�4TQ �� (k) 3�� $ � ê����������!� WCDRQ6D��C4TD8Q A�5 *K4 )��8, _ n!]TDF4 OZ2$@qDVA�0^] 5?<=@FAC<XD�E�G� L � g % %

B�@1a�A6 � f % <=]&DbOZ2�IKI�2���*+4CE ]T2$I#Q�5�<=@87 D��

#

Page 7: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

)+*-, n!]TD W62�4TQJ*K4&d$DF5?<=9�DB4&<�5 � [�b���[ = � i %&�������5�^[���Y = � i %B% A�5�5\2 0F*�AC<�D8Q���* <�]�g 5FAC<=*+5�O+G[�b )*��� b���1 A4TQ [Z( �Z� ( = %e)*� ���( OZ2�@ A�IKI � ( = %>� ( �

)K*+*-, n!]TDUA�5�5\2 0F*�AC<�D8Q���DVA�IZ<=]J;l@V2 08DF5�5 ����( � g �\� ( = %!"�(� = Q6D��C4TD8QRA�5k*K4 )���, 5BAC<�*K5 �&DB5 �

��( � g �\� ( = % )*� ���( OZ2$@ A�I+I � ( = %�� ( �)+*K*K*m,on!]TDb5?<�@BAC<�DFE�Ga5\D$<

B�K1a�A6 � f % *K5e4T2$4��XDB9s;[<-Ga*+O�A�4TQa2$46ImG�*KO f )*��� b ��1 _

���$%�%��0��?ÉÙ>ÝJØ_× ßIEÑ:<CGà �vC % â Ø�; $ � �4� ê$:<AJL�=@ÝJ?�A#:<ÜMÜJEGÖ�:<A�CGAJLJ�Jß7=KCFØ<A�:<;@�<�JàË?IAe=�ã1åa?I=� L � g % %

B�@1a�A6 � f %RH¹?g:<A�:<;@HMCG=K;@:<;>ÖÈÙt=K;K:Ê=K?��\Ö�ã �VCFAMß�? � � F G :<AJL"=KÝM?�;@?1CGÙ�AJØ CFAeá<?�Ù>=@àË?IAe=

CFA"=KÝM?g=@?�;>àËCGAO:<Eyܹ?�;>CFØ}L§ÞM=@ÝJ?gß�Ø�AJÙ>�JàÈÜM=KCGØ�A'ÜJEÑ:<A â Ø�;�ܹ?�;>CFØ}Lt� àÉ�JÙ>=ÆÙ@:\=KCGÙ â ÖN5�2� �'��#- �1���Y = [���Y = -�] D��Y = �:6H��-kI\� %�):3 � �A%

â Ø�;Æ:<EFE�� � = %c� � ã�< â � �µê�Þ�EF?7=p� ��Y == %c� ��Y = H ?·:<;>HJCG=@;K:<;tÖ+HJ�M=Æè &V?�Lyã ��ÝJ?�A � �A%�àÉ�JÙt=ÆÝJØ�EFLâ Ø�;É:\ArÖ`��� % � ã � ?�ß�:<EFEGCFAJ�'=KÝJ:\= � � F BGHG V F BG Þ%=@ÝJ?+EF:<Ù>=6=K?I;@à Ø�A�=@ÝJ?+;�ã ݧã Ù�ã�Ø â � �A%gCFÙAJØ�AVÛÐAJ?���:\=KChá�?|HM�M=�àË:_ÖÈH¹?�ßIØ�àË?|:<;@HMCG=K;@:<;@CGEGÖ Ù>à3:\EFE±ã <Ð= â Ø<EFEFØ_×�Ù,=KÝO:Ê=F� �$%�ß�:\A"Ø�AJEGÖ$H¹?0Ù@:\=KCGÙ>èO?ILâ Ø�; m���� ��� %�� C â �1���Y = [���Y = )Q���'���ã < â � � ê6=@ÝJCFÙ�;@? +r�JCF;>?�Ù [���Y = �Z�

��Y == % )*� ��,��Y = â Ø�;�:\EFE� ��Y == %�� ��Y = ×�ÝJCFEG? â Ø�; �4� êgØ�AJ?gàÉ�JÙt=ÆÝO:�á�?v[�b ) ��� b��Z1Éã9DØ_× EG?I= $#% �(3���ê��������&�!� � �\"�H¹?g:<;@HMCG=K;@:<;>Ö+:<AJL�:<Ù>Ù@�JàÈ?1=KÝO:\=�=@ÝJ?gß�EF:<CFà CFÙ�=@;@�J? â Ø�; $ - ê�ÞC±ã ?<ãhÞ8[Z( G = �Z�

( G == % )*� ���( G = â Ø�;�:<EGE �( G == %�� ( G = ã�CRÖ"ë0?IèOAJCh=KCGØ�A �

N ( G = � �'�( G = - �1,(�[Z(�-2] D( �L68( G = -kI�( G = %���[Z( G = �~] D( G = 68( G = �'�( G = - �1,(�[Z(�-2] D( �L68( G = -kI�( G = % - ���( G = � � #"%

5DÙ>CFAJ�È:$Ù@CFàÈCFEF:<;R:<;@���MàË?IAr=Æ:\ÙÆCGA"=KÝJ?1èO;>Ù>=ÆÙ>=@?�Ü�?�+r�O:\=@CFØ�A0� #"%q;>?�+r�JCG;@?�Ù�=@ÝO:\= â Ø�;�:<EGE���( G = %���'�( G = - �1,(�[Z( - �:68( G = -kI�( G = % D ]H(,- ���( G = ):3

:<AJL§Þ�=KÝM?�;@? â Ø�;@?\Þ �'�( G = - �1,(�[Z(,- ���( G = ) 3Mã /�Ø<; $ � 3È=@ÝJCFÙÆCFÙÆ?�+r�JChá\:<EF?IAr=D=KØ [Z( �Z� ( = %,) � �� (â Ø�;0:\EFE�� ( = % � ( ã < â $ � 33=KÝJ?É:<H Ø_á<? CFAJ? +}�J:<EFCh=�Ö�;>?�+r�JCG;@?�Ùz[�bv) ���� b���1Éã ��ÝMCFÙ0ÜJ;>Ø_á�?�ÙgßIEÑ:<CGà�vC %7ãF��ÝJ?$:<Ù>Ù@?�;t=KCGØ�A �vCGC %�CFÙ1:<A�CGàËàÈ?�LMCÑ:\=@?·ßIØ�AJÙ@? +r�J?�AJßI?ËØ â ��C %Æ:<AJL�?�+r�O:Ê=KCFØ<A � �"%ã���ÝJ? Ø�AJEhÖC â eÜO:<;t=qCGA ��CFCFC %�ß�:\A3H¹?DÜJ;>Ø_á�?�L"HeÖÈ�JÙ>CFAJ�·ë0?IèOAMCG=KCGØ�A �?��C %�:<AJLÈ=KÝJ?Æ;@?IÙ@�JEh= â ;>Ø�à �vC %k=@Ø�Ù>?�?D=@ÝO:\=f d ��� b���1 CFàÈÜJEGCF?�ÙPN be� f � [�b � ] D�6 f � [�b f -|�� b���1 d 3·Ù@�MßTÝ+=KÝO:\=R=KÝJ?Dß�Ø�AMLJCG=@CFØ�Af ) ��� b��Z1 CFÙ AM?�ß�?IÙ@Ù@:<;>Ö<ã ��ÝJ? {C â kÜJ:<;>=ÈCFA ��CFCFC % â Ø�EGEFØ_×�Ù â ;@Ø<à =KÝM? â :<ß7= =KÝO:Ê=3:\ÙÈÙ>ØVØ<A :<Ùf )*��� b �Z1µ=@ÝJ?1Ù@?7=

B�@1a�@6 � f %,ß�Ø�Ae=K:<CFAJÙ�=@ÝJ?1ÜJ�J;>?7ÛÐH Ø�AML"CFAeá�?IÙ>=KàÈ?�Ae=ÆÙ>=@;K:\=@?��<ÖË×�ÝJCFßTÝ'AJ?7á�?I;

CFAeá�?IÙ>=@ÙDCGA�:\ArÖ+;@CFÙB�eÖ':<Ù@Ù>?I=@Ù,/{�;3$:<AJL�ß�Ø�AJÙ>�JàÈ?�ÙÆØ�AJEGÖ3CFA+=@ÝJ?1=K?�;>àËCGAO:<E§Ü¹?�;>CFØ}L"Ø â EFC â ?\ã �

��ÝJ?È;@?�Ù>�JEG=@Ù â ;@Ø�à åa?IàËàË:�êÈ:<;@?$LJCG;@?�ß7=6ß�Ø�AJÙ>?�+r�J?IAJß�?IÙÉØ â =KÝJ?$LJ?7èOAJCG=@CFØ�A#Ø â :'Ù>=K;@:\=K?I�<Ö#:<AML:<;@?Æ=KÝr�JÙ�CGAJLJ?IÜ ?IAJLJ?�Ae=�Ø â :<AeÖ3ÜJ;>? â ?I;@?�AMß�?�ÙIÞO?I=@ß<ã���ÝJ? â Ø<EFEFØ_×�CGAJ�gß�Ø�;>Ø�EFEF:<;>Ö$CGÙRCGàËàÈ?�LJCF:\=K? â ;>Ø�àë0?IèOAMCG=KCGØ�A � :<AJL�åa?�àÈà3:+ê�ã� %��$%���������� '� O f � ��� b���1 <=]&DP5VD�<

B�K1a�A6 � f % 082�4T<ZA�*K4C5�Ap5S*K4CE I#D[58<=@FAC<XD�E�G � L � g % QCD��64TD3QfWVGR<�]TDhQ6D30B*K5S*�2$4

N&bX� 3 ��[Zb~� ��� b��Z1 ��] bX� 3 A�4TQo;lI A�465 N!( v 3���[Z( v � ���( A�4TQ ]H( v 3 OZ2$@/D\A�0^]$ � �������5�!�j_

!

Page 8: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

� ��� �� �� ����� �� � ��� ����� ���������5��

��Ø6LJ?I;@CGá<?�=KÝJ?Æß�Ø�AMÙ@�JàÈ?�; {Ù,LJ?Iß�CFÙ>CFØ�AÈÜJ;>Ø�HJEF?Ià ×R?DàË:4�\?D:\Ù@Ù@�MàËÜM=@CFØ�AMÙ�Ø�AËÝMCFÙ,?'&Vܹ?�ßI=K:\=KCGØ�AJÙ â Ø�;â �M=K�M;@?D:<Ù@Ù>?I=RÜJ;@CGß�?�ÙR:<AJLËLJCGá}CGLJ?�AJLMÙq:<Ù�×R?�EGE :\ÙRØ�AÈÝJCGÙ�ÜM;@? â ?I;@?IAJß�?IÙ�Ø_á�?�;q:<EG=@?�;>AO:\=KChá�?�ßIØ�AJÙ@�MàËÜVÛ=KCGØ�A�Ù>=@;@?�:\àËÙIã /�Ø<;|=KÝJ? â Ø<EFEFØ_×�CGAJ�+LJ?I;@CGá\:\=@CFØ�AMÙ1:<Ù@Ù>�JàÈ?$=@ÝO:\=0=@ÝJ?$Ù>=@;K:\=@?��<Ö�Ù>?I=

B�K1a�A6 � f %DCFÙ

AJØ�AVÛÐ?�àÈÜM=�Ö�ã � ?�ß�:<EFEÏ=KÝO:Ê=g:\=|=@CFàÈ?J� � 3Ë=KÝJ? ßIØ�AJÙ>�JàË?I;|=K;>?�:\=@Ù â �M=K�M;@?ÉÜJ;>CFßI?�Ù1:<AML�LJCGá}CFLM?�AJLJÙ� = �\� t �������M:<Ù�;K:\AJLJØ�à á<:\;@CÑ:\HJEF?IÙ�ã���ÝJ? â Ø�EGEFØ_×�CFAM� :<Ù@Ù>�JàÈÜM=KCGØ�A"ßTÝO:<;@:<ßI=@?�;@CG��?IÙÆÝMCFÙ�?'&Vܹ?�ß7=T:\=@CFØ�AJÙâ Ø�; â �M=@�J;@?6:<Ù>Ù@?I=DÜJ;>CFß�?IÙÆ:<AJL'LJCGá}CGLJ?�AJLMÙ�×�Ch=KÝJCGA'ÝJCFÙ�ÜJEF:<AJAJCGAJ� ÝJØ�;>CF�IØ�A§ã��� ��� "$ �%&� '� *Zd$DF4 <=]TDi;lI A�4646*+4CE ]T2�@�*��$2$4 � �;3 <�]TDH082�465?7:9�DB@�� 5HD�� ;[D80�< AC<�*�2$4C5kAC<h<�*K9�D ��� 3 OZ2$@hOX76<S7:@VDA�5�5\D$<�;l@S*�08DF5aA�4TQ Q�*Zd$*#Q6DB4&Q�5/A�@VDRE *Zd$DF4 WVG A ;T@V2 W ACW�*KI+* <-G 9RD\A�5?7�@VD��(2$4 <=]TDa9�DVA�587:@BACW�I�D;l@V2 Q&7 0�< 5Z;�A�03D�� � � �F� � � � %�� Q6D �646*+4CE A 5?7�W��8D30$<�* d$D��82$*K4&<k;l@\2 W A6W�*+IK*Z<-G Q�*+5?<=@S*�WC7C<=*�2�4 2�O <=]TD@BA�4&Q62$9 dVA�@S*�A6W�I#DB5 � = �������5�B� � _<�A3=KÝM?|Ù@? +r�J?�Ey×R?|LM?�AJØ<=@?|=KÝM?|ß�EF:<Ù@Ù�Ø â :\EFE�ÜJ;@Ø<HO:<HJCGEFCG=�Ö�àË?�:<Ù@�M;@?�ÙqØ�A � � � ��� � � � %��eÞ � )µê�ÞVHeÖ��;@Ø�H�� ��� %ã <�A�=@ÝJ? EFCh=K?I;K:\=@�J;@?6=KÝJ? �>Ø<CFAe=1LJCGÙ>=K;>CFHJ�V=KCFØ<A�Ø_á�?I; â �M=K�J;>?$:<Ù@Ù>?I=gÜJ;>CFßI?�Ù ��;@?�Ù>Ü ?IßI=@CGá�?IEGÖ:<Ù@Ù>?I=Ë;@?7=K�J;>AJÙ�%ÉCFÙ �MÙ@�O:<EGEGÖ«:<Ù@Ù>�JàË?IL =@Ø#H ?'Ø â =KÝM?�ÜM;@Ø}LJ�JßI= â Ø�;>à � � � =! ����� � �ÇÙ>�JßTÝ=KÝO:Ê=|=KÝM?�Ù@CG��AO:<EGÙp��(3:<AJLc��" :<;>?�ܹ?�;>ß�?�Chá�?IL�=KØ3H¹?�CGAJLJ?IÜ ?IAJLJ?�Ae=0×�ÝM?�AJ?7á�?�; $ ��*/�ã 9DØ+Ù>�JßTÝ:<Ù@Ù>�JàÈÜM=KCGØ�A'CFÙ�AJ?I?�LJ?IL�ÝJ?I;@?<ã��ÝJ?,ß�Ø�AMÙ@�JàÈ?�; {ÙcÜJ;@? â ?�;>?�AJßI?�Ù%Ø_á<?�;c:<EG=@?�;>AO:\=KChá�?kßIØ�AJÙ>�JàËÜV=KCFØ<A6Ùt=K;>?�:<àÈÙc:<;@?�ßTÝO:\;K:<ß7=K?�;>CF�I?�L6AJ?'&}=�ã��� ��� "$ �%&� �� *Zd$DF4�<=]&D[;TI�A�464C*K4CE ]T2$@S*��$2$4 � �;3 � <�]TD 082$46587:9�DB@#� 5�;l@VDFOZDB@VDF4T08DF5p2:d$DF@ 082�465?7:9s;[<�*�2$4 ��* <�]6*K4]6*K5e@\DB9fA�*K4C*K4CE�I+*KOZD$<�*K9�Dp0\A�4`W6Dp@VD�;l@VDF5VDF4T<�D8QjWVGj<�]TD�76<=*+IK*Z<-G�OX7:4&0$<=*#2$4

�=N b��BN = ���������BN&� %%$ �lY & �=N b�% - �'( =)(

( & ��N (4% � !$%

Q6D��C4TD8Q 2$4 � � G = ��*Z<=] Q�*+5V082�7:4&<�O�A 0$<X2�@ ( � 36_ n!]TDJ*K4C5?< A4T<ZA�4TD32 7:5a76<=*+IK*Z<-GoOX7�4T0$<�*�2$4 & � �TY F *+5H082$4&<=*+4&7 2 7:5 � 5?<=@S*�0�<=ImG�*K4T0F@VD\A�5�*+4CE � A�4&Qf58<=@S*�0$<�ImG>082$4T0\A d$D _

/OØ�;�?�:\ßTÝ�Ùt=K;@:\=K?I�<Ö � L � g % %B�@1a�@6 � f %�:<AJL/� � = %�� � ÞJLJ?IèJAJ?1=KÝJ?0�V=KCFEGCG=�ÖË:\=>=T:<CGAJ?�L"Ø_á�?I;�=KÝJ?

;@?Ià3:<CGAJCFAM�ÉEFC â ?I=KCGàË?

* b(� L �\� � = %qÚT�+& �=N b.% - �'(� = (

( & �=N!( �Z� ( = %B%&���ÝJ?6?'&VÜ ?IßI=@?�L��V=KCFEGCG=�ÖËCFAJLM�Jß�?IL�HeÖ"Ùt=K;K:Ê=K?��\Ö1� L � g % %

B�@1a�A6 � f %qCFÙ�=@Ýr�JÙD�<CGá�?IA'HrÖ,�-/.0*�b � L � i %21 �436587�* b(� L �\� � = % � �@I � � = % � � 2"%

/OØ�;�?�:<ßTÝ0�@1a�@6 � f % â Ø<;�×�ÝJCFßTÝB�@1a�@6 � f % ��:9ËEG?I=

;HbD�K1a�A6 � f %qÚC� Ù@�JÜ=<>,?-/.@* b(� L � i %A16BBBB � L � g % %B�@1a�A6_� f %DC � � >$%

2

Page 9: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

��ÝJ?6LJ?IèOAMCG=KCGØ�A"Ø â :<A�Ø�ÜM=KCGà3:\E Ùt=K;K:Ê=K?��\Ö'CFÙ�AJØ_× Ùt=K;@:<CF��Ýe= â Ø�;>×q:<;@Lyã�������! #"$ #%&���� *Zd$DF4�AJ<�@�*{;lI�D �K1a�A6 � f % ��*Z<=]

B�@1a�@6 � f % ��+9 � A�5?<�@BAC<�DFE�G � L�� � g�� % %

B�@1a�@6 � f % *+5p<�DB@S9RD3Q

A�4 Ø�ÜM=KCGà3:\E Ùt=K;K:Ê=K?��\Ö *KO ,?-/.@* b(� L � � i %A1 �4; bD�K1a�A6 � f % ��* <�] ;HbD�K1a�A6 � f % W6DF*K4CE�Q6D �64TD3Q�*K4 )��?, _

��ÝJ?gß�Ø�AMÙ@�JàÈ?�; {Ù�Ø�H��>?IßI=@CGá�?gCGÙq=KØ ßTÝJØ}Ø�Ù>?·:\A�Ø<ÜM=KCGà3:<E¹Ù>=@;K:\=@?��<Ö�� L�� � g�� % %B�@1a�A6_� f %RCGA+=KÝJ?

Ù@?IAJÙ@?·Ø â ë0?7èOAJCh=KCFØ<A Mã�/OØ�;@àË:<EFEhÖ$ÝJCFÙ�LJ?Iß�CGÙ@CFØ<A�ÜM;@Ø�HJEG?�à :\=�=KCGàË?z��� 3 à3:�Ö3H ?gÙ>=K:\=K?IL�:\Ù

àË:(&;�� � ?

< ,?-/.@* b(� L � i %A1 BBB � L � g % %B�@1a�A6_� f % C � ��ì$%

<Ð=�CFÙ�ßIEF?�:<;q=KÝJ:\=�=KÝM?1ÜJ;@Ø�HMEF?�à ��ì"%RCFÙ�Ø<AJEGÖÈ×q?IEFEoÛ�LJ?7èOAJ?�L'C â =@ÝJ?1Ù@�MÜJ;@?IàÉ�Jà CGA � >$%�CFÙqèOAMCG=K?\ÞJC±ã ?<ãhÞC â ;HbD�@1a�A6_� f % d� ã%� ÝJCFEG?R=@ÝJCFÙ�CGÙk=K;@Chá}CÑ:<EGEGÖgÙK:Ê=KCFÙtèO?�L â Ø�;k=@ÝJ?�ß�:\Ù@?�×�ÝJ?�;>?�=KÝJ?��M=@CFEFCh=�Ö â �JAJßI=@CFØ�A*�CGÙ0H Ø<�JAJLJ?IL �v:<Ù0CGÙ0Ø â =K?IA#:<Ù@Ù>�JàÈ?�L#CFA�=@ÝJ? EFCh=K?I;K:\=@�J;@? %7Þ =@ÝJCFÙ|;@?�+r�JCG;@?IàË?IAr=|=K�J;>AJÙ1Ø��M=0=@Ø"H ?=KØ}Ø�Ùt=K;@Ø<AJ��CGA3àË:<AeÖ$Ù@ß�?IAO:<;>CFØ�ÙIã���ÝJCFÙ�CFÙ â Ø�;�?'&M:<àÈÜJEF?�=KÝJ?Dß�:<Ù>?D×�Ch=KÝ+:6Ü Ø_×R?�;R�M=KCGEFCG=�Ö â �JAJßI=@CFØ�A×�ÝJCFßTÝ�CFÙ�Ùt=K�JLJCG?�L�CFA �V?�ß7=KCGØ�A �Mã���ÝM? â Ø�EGEFØ_×�CFAM�$:<Ù@Ù>�JàËÜV=KCFØ<A�Ø��y?I;@ÙÆ:<A�:<EG=@?�;@AJ:\=KChá�?1ÜJ;>Ødá}CGLJCFAJ�=�×qØÈÙ@���ËßICF?IAr=Dß�Ø<AJLJCG=@CFØ�AMÙ â Ø�;�=KÝJ?gLJ?Iß�CGÙ@CFØ<A�ÜM;@Ø�HJEG?�à ��ì$%R=@ØËH¹?0×q?IEFEoÛ�LJ?7èOAJ?�Lyã��� ��� "$ �%&���.�<�I�DVA5?<i2$4TD�2$Oi<=]&DbOZ2�IKI�2���*+4CER< ��2J032$4TQ�*Z<=*�2�465e*K5e5FAC<=*+5 �TD3Q �

)+*-, n!]TD 76<=*+IK*Z<-G OX7�4T0$<�*�2$4 & *+4R.b5�587:9s;[<=*#2$4 ��*+5 W62 7�4TQ6D8Q _

)K*+*-, n!]TDk9�DVA5?7:@\D �f*K4J.b5S5?7:9s;[<=*#2$4��p] A�5 032$9s;�A�0$<!5?7?;C;�2$@8<��� = VN������V �� � % � � � � % ��* <=]DVA 0^] �� (�� � � $ �&����������� � WCDB*+4CE�082$9s;�A�0�< _

��ÝJ?0;>?�+r�JCF;>?�àÈ?�Ae=�CGA��vCGC %%=KÝJ:\=q=@ÝJ?|Ù>�JÜJܹØ�;>=�CGÙ�=@ÝJ?0ÜJ;>ØVLM�JßI=qØ â ß�Ø<àËÜO:\ßI=�Ù>?I=@Ù�CFÙRà3:<LM? �>�JÙt= â Ø�;ß�Ø�Aeá<?�AJCG?�AJßI?<ãF<�A�ÜJ;@CGAJß�CGÜJEF?\Þ Ch=|Ù>���Èß�?IÙ0=KØ":<Ù>Ù@�JàÈ?�=@ÝO:\=|=@ÝJ?ÉÙ>�JÜJܹØ�;>=1Ø â � CFÙ0:Ëß�Ø�àÈÜO:<ß7=0Ù@?7=�ã��ÝJ? â Ø�EFEGØ_×�CFAJ�0EG?�àÈà3:DÙ@ÝJØ_×�Ù�=KÝO:Ê= �vCFC %cCGA - Ù@Ù>�JàËÜV=KCFØ<A 0CGÙ�CFAJLM?�?�L$Ù>���Èß�CF?IAe= â Ø�;�=KÝJ?�LJ?Iß�CFÙ>CFØ�AÜJ;@Ø<HJEF?Ià =KØ$H¹?g×R?�EGEhÛÐLJ?IèOAM?�L�?Iá�?IA�C â *&CGÙ�AJØ<=ÆH Ø<�JAJLJ?IL§ã ��ÝM?·ÜJ;>ØVØ â CGÙ���CGá<?�A�CFA �V?�ß7=KCGØ�A - ãhêCFA - ÜMÜ ?IAJLJC & - Ø â =@ÝJCFÙ�ßTÝO:\ÜM=K?I;�ã�M������� �� D$<p.p5�587:9�;�<=*�2�465�� � ��A�4TQ�� W6D 5BAC<�*K5 �TD8Q _ n!]TDB4 <�]TD�587?;l@VDF9�7:9 Q6D��C4TD8Qx*+4()��8, 5BA <=*K5 �TDB5; b �@1a�A6 � f % d� OZ2$@ A�I+I �@1a�@6 � f % OZ2$@��]6*�0^]

B�K1a�A6 � f % ���� _

<�A�=KÝJ?ÉÙ>?�+r�J?IEk×q? Ù>ÝO:<EFE%:<Ù@Ù>�JàÈ?�=KÝO:Ê= - Ù>Ù@�JàÈÜM=KCGØ�A 3CGÙ0ÙK:\=@CFÙtèO?�L#Ù@�MßTÝ#=@ÝO:\=0=@ÝJ?ÉßIØ�AJÙ@�MàË?I; ÙLJ?�ßICFÙ>CFØ�A ÜJ;@Ø<HJEF?Ià ��ì$%+CFÙ"×R?�EGEhÛ�LM?IèOAJ?IL§ã - Ù@Ù@Ø}ß�CF:\=K?IL ×�Ch=KÝ : Ù@Ø<EF�M=@CFØ�A =KØ ��ì$%+LJ?7èOAJCGAJ� :\AØ�ÜM=@CFàË:<E�Ùt=K;@:\=K?I�<Ö � L � � g � %DCGÙ1:<A#Ø�ÜM=@CFàË:<EÏLJ?�ßICFÙ@CGØ�A �=N � b �!W �b % % � VOS â Ø�;z�,� 3Mã ��ÝJ? àË:<CFA��Øe:<EÏØ â =KÝJ? â Ø�EFEGØd×�CGAJ�$Ù@?IßI=KCGØ�A�CGÙÆ=@Ø3Ùt=T:\=@?�ß�Ø<AJLJCG=@CFØ�AMÙD�JAMLJ?�;Æ×�ÝJCFßTÝ�=@ÝJCFÙÆØ�ÜM=@CFàË:<EaLJ?Iß�CFÙ>CFØ�A�CFÙ×q?IEFEoÛ�LJ?7èOAJ?�L':\AJL+ß�:\A+H ?|;@?�ÜM;@?�Ù>?�Ae=K?IL'HrÖ3:�ßIØ�Ae=KCFAr�JØ<�JÙ â �JAJß7=KCGØ�A+LJ?IÙ@ß�;>CFHJCGAJ��=@ÝJ?|ßIØ�AJÙ@�MàË?I; ÙLJ?�àË:<AJL�H¹?�ÝO:�á}CFØ�;�CGA"=KÝJ?gLJ?Iß�CFÙ>CFØ�A'ܹ?�;>CFØ}L§ã

>

Page 10: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

� ��� ��� � ��� ��� ���� �E��� �$����=���������

æqØ�AJÙ>CFLJ?I;kAJ?'&}=k=@ÝJ?qLM?�;@Chá\:\=KCGØ�A�Ø â :<AÉØ�ÜM=@CFàË:<ErÙ>=@;K:\=@?��<Ö6LJ?7èOAJCFAM�g:DÙ@Ø<EF�M=@CFØ�A6=KØ|=@ÝJ?qßIØ�AJÙ@�MàË?I; ÙLJ?�ßICFÙ>CFØ�A�ÜM;@Ø�HJEG?�à�ã �VCFAJßI?·=@ÝJCFÙ�=T:<ÙB��=@�J;@AMÙ0Ø��M=Æ=KØ+H¹?·=@;@CháVCF:<EaCFA�=KÝJ?�ß�:<Ù>?�×�ÝJ?�;>? f �}��� b �Z1�vÙ>?�?�æqØ�;@Ø�EGEÑ:<;tÖ êD%7ÞR:<Ù@Ù>�JàÈ? â Ø<;�=KÝJ? â Ø�EGEFØ_×�CFAM��LJ?�;>CGá\:\=@CFØ�AJÙ·=KÝO:\= f � ��� b���1Éã ä�àËÜMEFØ_Ö}CFAJ�:3;@?Iß��J;>Ù@Chá�? Ù@Ø<EF�M=@CFØ�A�=K?�ßTÝMAJC,+r�J? â ;>Ø�à Ùt=KØ}ßTÝO:<Ùt=KCFß·LMÖ}AO:<àÈCFß·ÜJ;@Ø��<;K:<àÈàËCGAJ�JÞ�CG=Æ×�CFEGEÏH ?ÉÙ>ÝJØ_×�A=KÝO:Ê=g�JAJLJ?I;1Ù@Ø�àÈ? àËCGEFL�:<LJLJCh=KCFØ<AO:<Ec;@?�Ùt=K;>CFßI=@CFØ�AMÙ1:+ß�Ø�Ae=@CFAr�JØ��JÙgLJ?Ià3:\AJL â �JAJßI=@CFØ�A�LM?�Ù@ßI;@CGHJCFAJ�=KÝJ?|Ø�ÜM=KCGà3:\E¹ßIØ�AJÙ>�JàËÜV=KCFØ<A":<AJL+CGAeá�?�Ùt=KàÈ?�Ae=�LJ?Iß�CFÙ>CFØ�A â Ø�; ��� 3�ß�:<A"H ?|LJ?IèOAM?�L§ã �cØ :<EFEG?Iá}CÑ:Ê=K?=KÝJ?ÈÙ@�MHJÙ@? +}�M?�Ae=$AJØ<=K:\=KCGØ�A�×q?ËLJ?IèOAM? â Ø�;g?�:\ßTÝX] %�F B :<AML ��� �L6 �!I�% % � =@ÝJ?ËØ<Ü ?I;K:\=@CFØ�A]�� �6ÚC�U] D��:6c-kI�%�:<AJL'=KÝM? â �MAJßI=@CFØ�A�� ÚlS V � V F G V F GHG �TY F Þ

� � � [ �^] % �\�����'�� �1 ��ÚC� �' - �1#[�-2]�� �l� �Yê 3$%égChá�?IA ?.&VÜ ?IßI=T:Ê=KCFØ<AJÙ �'�( G = ) 3MÞ �1,(�� 3':<AJL :"ܹØ�;>= â Ø�EFCGØ�W�( % S ÜJ�J;@ßTÝJ:<Ù@?IL«:\=1=@CFàÈ? $ =KÝJ?á\:<EF�J?�� �@W�( �\��( G = �\�'�( G = � �1 ($%�LJ?�Ù>ß�;@CGH ?IÙ|=KÝM?Éß�Ø�AMÙ@�JàÈ?�; {Ù|×R?�:\EG=KÝ�CFA�ܹ?�;>CFØ}L $ - êÉLJ?IÜ ?IAJLJCFAM�Ø�A ÜJ;@CGß�?�Ù�68( G = :\AJL�LMCGá}CFLJ?IAJLJÙjI�( G = ã���ÝM? â Ø�EGEFØ_×�CFAM�+LJ?IèJAJCG=@CFØ�A#CFAe=@;@Ø}LJ�Jß�?IÙ1=KÝJ?$ß�Ø<AJß�?IÜM=�Ø âAJØ�AVÛÐ;@?ILJ�JAJLO:\Ar=|:<Ù>Ù@?I=@ÙÆ=@ÝO:\=�×�CGEFEyH¹?�ßIØ�àÈ?6CGàËܹØ�;t=T:<Ae=�CGA"=KÝJ?gÙ@? +r�J?�E�ã�������! #"$ #%&��. ;l@V2 W:A6W�*KI+* <-G 9RD\A�5?7�@VD ���2$4 � � ��� � � %)% *+5k5BA�*#Q�<�2 *+4TQ&7 03Dp4T2$4 ��@VD8Q 7:4TQ A�4&<iA�5�5\D$<�5b*KO!OZ2$@bD\A�0^]W� �!W� % S ��W� �� W� <=]TD 5VD�<� �KW� �!W� %ÈÚT���l� % ��� � �KW�C�B�l� 3���êD% �� � �@W� �\����3���êD%�� % � � � %5BAC<�*K5 �TDB5 �� � �@W �!W %B%e�;36_��ÝJ?|ÜM;@Ø�ܹ?�;t=�ÖËØ â AJØ�AVÛÐ;@?ILJ�JAJLO:\AJßIÖË?�AJÙ>�J;@?IÙq=KÝJ:\=R=�×RØÉLJCGÙ>=@CFAJß7=qܹØ�;>= â Ø�EFCGØ�Ù�ß�:\A3AJØ<=RCFAMLJ�Jß�?Æ=KÝJ?ÙK:<àÈ?,;@?7=K�J;>A·×�CG=@Ý·ÜM;@Ø�HO:\HJCFEGCG=�ÖDØ�AJ?<ã ��ÝJCFÙÏßIØ�AJLJCh=KCFØ<Ag×�CGEFE<=@�J;@A6Ø��M=Ï=@ØDH¹?,AJ?�ßI?�Ù@Ù@:<;>Ö·CFAgØ�;>LJ?�;Ï=KØØ�HM=K:<CFA+LM?�àË:<AJL â �JAJß7=KCGØ�AJÙ�ã <�Ar=@�JCG=@CGá<?�EGÖ<ÞMCh=�CFÙRß�EG?�:<;�=KÝO:\=�Ø<=KÝJ?I;>×�CGÙ@?|=@ÝJ?0ß�Ø<AJÙ@�JàÈ?�; {Ù�ܹØ�;t= â Ø�EGCFØLJ?�ßICFÙ>CFØ�A à3:�Ö�AJØ<=6H ?È�JAJC�+r�J?�EhÖ�LJ?I=@?�;>àËCGAJ?�L§ã�9ÆØ<=K? =KÝJ:\=g=KÝJ?ÈÜJ;@Ø<Ü ?I;>=�Ö�Ø â AJØ�AVÛÐ;@?ILJ�JAJLO:\AJßIÖLJ?�ܹ?�AMLJÙÉAJ?ICG=KÝM?�;6Ø�A�=@ÝJ?3?.&Mܹ?�ß7=K?ILçAJØ�AVÛÐß�:<ÜJCh=T:<E�CGAJß�Ø<àË?$AJØ�;6Ø�A =@ÝJ?ÈH Ø�AML ;@?7=K�J;>A ×�ÝJCGßTÝ«CFÙ=KÝJ?g;>?�:<Ù>Ø�A�×�ÝeÖ"=@ÝJ?IÖ'ÝO:�á<?·H¹?�?IA�Ù>?I=�=KØ$��?I;@ØË:<AJL��JAJCh=�Ö"CFA+=@ÝJ?gLJ?IèOAMCG=KCGØ�A§ã�M������� �� D$< ��fWCDMAP;l@V2 W:A6W�*KI+* <-GU9RD\A�5?7:@\Di2�4 � � �F� � � %)% A4TQ ��·Ú � �TY � WCDh<=]TD�*�Q6DF4&<=* <-G _�� 78;6;�2�5VDk<�] AC<<=]TD dVA�@�* A�4T08D �X032 dVA�@S*�A�4&08Dp9 A <=@�* � �� ÚT� ,��-�� ���� � ,��- .@�� 1 % �������,��- .@�� 1 % D�� D � *K58<=5HA�4TQ�*+5r;[2$5S* <=*Zd$DQ6D��C46* <�D _ n!]TDB4 ��R*+4TQ&7 03DB5k4T2$4��=@VD3Q&7:4TQ A�4&<iA5�5VD�<=5 _���$%�%��,��?DÙ>ÝJØ_×Í=KÝO:Ê=RßIØ�Aeá�?I;@Ù@?IEGÖËC â =KÝJ?�àÈ?�:<Ù>�J;@?3�� LJØV?IÙRAMØ<=�CFAJLJ�Mß�?ÆAJØ�AVÛÐ;@?�LM�JAJLO:<Ae=q:<Ù@Ù>?I=@Ù=KÝJ?IA+=KÝJ?Æá\:<;@CF:<AJß�?Û�ßIØdá\:<;>CÑ:<AMß�?�à3:Ê=K;@C & �� ß�:<AMAJØ<=�H¹?|ܹØ�Ù>CG=KChá�?ÆLJ?IèJAJCG=@?<ã��cØ�=KÝJCGÙR?IAJL§ÞVÙ@�JÜJܹØ�Ù>?=KÝJ?I;@?$?'&VCGÙ>=6Ü Ø<;>= â Ø<EFCFØ<Ù�W� � �K[� �M] %&��W� � �K[� �M] % % S0Þ_W� �� W� �Ù>�JßTÝ�=@ÝO:\= � �@W� �`�����3���ê %��� �@W �`�����3���êD%�� 3N�� ÛÏ:Mã{ÙIã�åa?I="!�WËÚT�gW �0W �� 3g:<AMLÈLM?IèOAJ?0���:<Ù�:<H¹Ødá<?<ã�9ÆØ<=K?�=@ÝO:\=�] ��U] �vØ<=@ÝJ?�;t×�CFÙ>?c] � ] y×qØ��MEFL�CGàËÜJEhÖ3[� ��Q[� y×�ÝMCFßTÝ�CGÙ|AJØ<=|Ü Ø<Ù@Ù@CGHJEF? %7ãDåa?I=#!a] ÚC�9] 8��] �� 3:<AJLqN|ÚT�g[�^��[� }:<AJL LJ?7èOAJ?�=KÝM?�;K:<AMLJØ�à á\:<;>CÑ:<HMEF?$! � Ú � �TY F Þ%! � �Z�D%qÚC�&!7]'�a��ã���ÝJ?IA! � ����D% � N0�� ÛY:Mã Ù�ãk:<AJL§ÞrEF?7=@=@CFAJ�)( ÚC� .+* B �,* B 1 %NF B�- t B ×�ÝJ?I;@?.* B CGÙ�=KÝJ?z+ V+ CGLJ?�Ae=KCh=�Öà3:Ê=K;@C & 3J�0/1�- .+! � ����D%A1 ��!7] D2( ,��-3� ����,� ,��- .@�� 1 %����� ��,��-/.@�� 1 %MD � (4!a]3�5!a] D2( ��$(6!7]Ïã��

ì

Page 11: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

��ÝJ?�ÜM;@?Iá}CGØ��JÙÆÜJ;@Ø}Ø â àË:<LJ?gØ�Heá}CFØ<�JÙÆ=@ÝO:\=Æ=KÝJ?6;@? +r�JCF;>?�àÈ?�Ae=|Ø â åa?�àÈà3:� =KÝO:\= �� H¹?·Ü¹Ø�Ù>CG=KChá�?LJ?IèJAJCG=@?6ß�:<A�H ?1×R?�:4�\?�AJ?IL�:<Ù â Ø�EFEGØ_×�Ù�ã� %��$%���������� �� D$< ( ÚT� . * B �,* B 1 %NF B�- t B _ � OP7:4&Q6DB@U<�]TDe]:G ;[2 <=]TDF5VDF5b2$O � DB9q9 A �q<=]&De9fAC<=@S* � ( �� (ND *K5;�2�5�* <�* d�DUQ6D��64C* <XD � <=]TDF4 ���*K4&Q&7 08DF5p4&2$4 �=@\D8Q&7�4TQ A�4&<MA�5�5\D$<�5 _égChá�?IA =KÝJ?3;K:<AJLMØ�à á<:\;@CÑ:\HJEF?X��3×�CG=@Ý«LJCFÙt=K;>CFHJ�M=@CFØ�A*�� æqØ�;>Ø�EFEF:<;>Ö �'?�Ù>Ù@?�Ae=@CÑ:<EGEGÖ ;@? +}�MCF;@?IÙÉØ�AJEhÖ=KÝO:Ê=�=@ÝJ?ÆCFAJLJ�Mß�?�LËLJCFÙt=K;>CFHJ�M=@CFØ�A$Ø â =KÝJ?Æß��Mà$ÛÐLJCGá}CFLM?�AJLÈÜJ;@CGß�?IÙ � ÚT�5(4��DÝJ:<Ùq:gܹØ�Ù@Ch=KCGá<?�LJ?IèOAMCG=K?á\:<;@CF:<AJß�?Û�ßIØdá\:<;>CÑ:<AMß�?1àË:\=K;>C & ã��ÝJ?6Ù@�JHJÙ>?�+r�J?IAr=g;>?�ßI�J;@Ù>CGá�?6Ù@Ø<EF�M=@CFØ�A'Ø â =KÝJ?gß�Ø<AJÙ@�JàÈ?�; {ÙDLJ?�ßICFÙ>CFØ�A'ÜJ;>Ø�HJEF?Ià5;@? +r�JCF;>?�Ù�=KØÈßTÝO:<;tÛ:<ßI=@?�;>CF��? â Ø�;�?�:<ßTÝ $ )µê�=KÝJ?�ßIØ�AJLJCh=KCFØ<AO:<EJLJCGÙ>=@;@CFHM�M=KCGØ�A Ø â =KÝJ?�;K:\AJLJØ�à á\:<;>CÑ:<HMEF?k��(gLJ?IÜ ?IAJLJCFAM�Ø�A�=@ÝJ?qÜJ;>?Iá}CFØ<�JÙ%Ø�HMÙ@?�;tá\:\=KCGØ�AJÙ�� = ���������B��(yY = ã%æqEF?�:\;@EGÖ<Þ<C â �{�&ê�ÞÊ=KÝJCGÙc=K:<Ù)�6CFÙÏ=K;>CGá}CÑ:<E�ã < â � � ê�Þ=KÝJ? â Ø�EGEFØ_×�CFAM�0EF?IàËàË:|LJ?IÙ@ß�;>CFH¹?�Ù�ÝJØ_× =@ÝJ? �>Ø�CFAe=�ÜJ;>Ø�HO:<HMCFEFCh=�Ö�LMCFÙ>=@;@CGHJ�M=KCGØ�A � CFAe=K;>ØVLM�Jß�?ILËCGA - ÙtÛÙ@�JàÈÜM=@CFØ�A�ê·ß�:<A�H¹? â :<ß7=KØ�;>CF�I?�L�CGAe=KØ3ßIØ�AJLJCh=KCGØ�AO:<E§ÜM;@Ø�HO:\HJCFEGCG=KCG?�Ù�:<AML�:ËàË:<;>��CFAO:\E§ÜJ;@Ø<HO:<HJCGEFCG=�Ö<ã��ÝJ?6ÜJ;@Ø}Ø â CFÙ���Chá�?IA�CGA*�}?�ßI=@CFØ�A - ã � CFA - ÜMÜ ?IAJLJC & - Ø â =@ÝJCFÙ�ßTÝO:\ÜM=K?I;�ã�M������� �� D$< � � ê A�4TQ � � F BGHG V F BG _ n!]TDB@\D/D��C*+5?<�5fA�O�A�0�<X2$@S*��?AC<=*#2$4 2$Os<=]TDq9�DVA�587:@VD � *K4&<X2082$4&Q�* <�*�2$4 AIP;l@V2 W:A6W�*KI+* <�*�DB5�� ( Ú � ( Y = V � � � % �TY . 3 ��ê 1 � $ � � ����������� � A�4&Q Ax9fA�@^E *K4 AI;l@V2 W A6W�*+IK* <-G � = Ú � � � % �lY . 3���ê 1 587 0^]o<�] AC<�OZ2$@bD\A�0^]�� % � � � � % �

� � � % � 3 5 i�i�i 3 5�'�� �=� � = % � � �Z� ��Y == �!I ��� % i�i�i � t �Z� = �!I � t % � = �@I � = %&� �Yê�êD%

n!]TDbO�A�0$<�2$@�* ��AC<�*�2$4 *+5 � � A _ 5 _ 7�46*�C7 D _/OØ�;�?�:<ßTÝ $ � �`�������&�!� =@ÝJ?6à3:<Ü � (8�Z� (yY == � i %�Ú � � � %��lY . 3���ê�1ÏLJ?IèOAM?�Ù|=@ÝJ?�ßIØ�AJLJCh=KCFØ<AO:<E§LJCGÙtÛ=K;>CFHJ�M=@CFØ�A Ø â =@ÝJ?�;K:<AMLJØ�à á\:<;>CÑ:<HMEF?e��(1LM?�ܹ?�AJLJCGAJ�gØ�A =KÝJ?�ÜJ;>?Iá}CFØ<�JÙ�Ø�HJÙ>?�;>á\:\=@CFØ�AMÙM� = ���������B��(yY = Þ×�ÝJCFEG?6=@ÝJ?�àÈ?�:\Ù@�J;>? � = LM?IèOAJ?IÙ0=KÝJ?·à3:\;@��CGAO:<EaLJCGÙ>=K;>CFHJ�V=KCFØ<A�Ø â =KÝJ?É;@:<AJLJØ<à á\:<;>CÑ:<HMEF?s� = ã ��ÝM?â Ø�EFEGØ_×�CFAJ� :\Ù@Ù@�MàËÜM=@CFØ�A'CGàËܹØ�Ù@?IÙ�Ù@Ø�àÈ?g:<LJLMCG=KCGØ�AO:<E ;@?IÙ>=K;>CFß7=KCFØ<AJÙ�Ø�A"=KÝJ?IÙ@?6LJCFÙt=K;>CFHJ�M=@CFØ�AMÙ�ã��� ��� "$ �%&� �n!]TD!;l@\2 W A6W*KIK*Z<-G Q�*+5?<�@�*�W 76<=*#2$465� ( �Z� (ZY == � i % � $ � � �������&�!� A�4&Q � = QCD��64TD3Q 2$4�<�]TD�9�DVA�587:@BACW�I�D5 ;�A 08D � � �F� � � %B% 5FAC<=*+5�O+Gj<�]TDpOZ2$IKI#2 ��*+4CEJ032$4TQ�*Z<=*#2$465 �

)+*-,��MA�0^]�� ( ] A�5 <�]TDpOZ2$IKI#2 ��*+4CE� lDBI+I�DF@�K;T@V2V;[DB@8<-G )KOZ2�@bQ6D$<ZA�*KI+5 � 5\D8D � <X2���DSG�� � 7 0\A�5 �������8,�� l2$@�DVA 0^] WC2 7:4TQ6D3QxA�4&Qj032$4&<=*K4&7 2�7:5sOX7�4T0$<�*�2$4�� Ú�� V � ( �TY F ��* <=] � � F " <=]TD*K4&<�DFE @FA�I[OX7:4T0�<=*#2$4 ( � ] �\� (yY == %6ÚT��� 5 � � ] �\� (ZY == �\�D% � ( �Z� (ZY == �!I �(% *+5 AE A�*+4 W62�7:4TQ6D3Q A�4&Q082�4T<�*K4&7 2 7�5U2�4 � V � (yY = _

)K*+*-,��MA�0^] 082�4TQ�* <�*�2$4�A�IrQ�*K58<=@S*�WC76<�*�2$4�� ( �=� (ZY == � i % A5 ��DBIKIrA�5f<=]TD 9 A�@^E *K4�A�IiQ�*+5?<=@S*�WC7C<=*�2�4 � =*K4&Q&7 08DF5k4T2$4 ��@VD8Q 7:4TQ A�4&<iA�5�5\D$<�5p*+4j<�]TDp5VDF465VD 2$O sD��646*Z<=*#2$4�� _

ê 3

Page 12: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

æqØ�AJÙ>CFLJ?I;kAJØ_× =KÝJ?R?'&VCFÙt=K?�AMß�?�Ø â :|Ù>Ø�EF�V=KCFØ<A·=KØÆ=KÝJ?qß�Ø�AJÙ>�JàÈ?�; ÙkLJ?Iß�CGÙ@CFØ<AÉÜJ;@Ø<HJEF?Ià �vì$%7ã 5DÙ>CFAJ�1:×q?IEFEoÛ �rAJØ_×�A+LMÖ}AO:<àÈCFß�ÜJ;>Ø���;@:<àËàÈCFAM�g:<ÜJÜJ;>Øe:<ßTÝ3=@ÝJ?|Ø�;>CF��CGAO:<E��*-«êIÛ�ܹ?�;>CFØ}LËLJ?Iß�CGÙ@CFØ<A3ÜJ;>Ø�HJEF?IàCFÙ�Ù@ÜJEGCG=RCFAe=KØ�:·Ù>?�+r�J?�AMß�?gØ â � -çê0Ø�AJ?Û�Ùt=T:<��?ÆÜJ;>Ø�HJEF?IàËÙIã �VCGAJß�?Æ=KÝJCGÙqCFÙR:<�e:\CFA$=K;@Chá}CÑ:<EOC â �4� ê�Þ:<Ù@Ù>�JàÈ? â Ø�;�=KÝJ? â Ø<EFEFØ_×�CGAJ�$LJ?�;>CGá\:\=KCGØ�AJÙ�=KÝO:Ê=�� � ê<ã@�cØ":<EFEG?Iá}CÑ:Ê=K?1=KÝJ?�Ù@�JHJÙ>?�+r�J?IAr=6AJØ\=T:\=@CFØ�A×q?�Ù>?I=�� ( � f �A6 %�ÚC� � ��Ny�^[ �^] % % � V2P VkR BB N�-*[0-*] D 6*� f �N[ ) � ���(�� â Ø�;3?�:<ßTÝ$ � ê��������5����ã ë0?IèOAM?'=@ÝJ?"á\:<EF�J? â �JAMßI=KCGØ�AJÙ=;8( Ú .L� ���(��

.vV � ( �TY F ;>?�ßI�J;@Ù>CGá�?IEGÖçHeÖ

Ù@?7=@=KCGAJ��; �@� f ���\� � = %�ÚT�+& � f ��%�:<AML â Ø�;�?�:<ßTÝ $ ��ê��������5�!� � ê

;H( � f ( �\� ( = %qÚC� à3:(&;�� �E?����\;� �� ���5? <%& ��N�%_- ( 3 5 ;H( G =�� � �KW��\���l�'�( G = � �1,(4%&�B� ( = �\��� � ( G = �Z�

(= �!I �D% C �

�Yê �"%<�A�=@ÝJ?1EFCh=K?I;K:\=@�J;@?|=@ÝJ?1;@?Iß��J;>Ù@CGØ�A �Yê �"%RCGÙ�ß�:<EGEF?ILCq?�EGEFàË:<AJA Ù�?�+r�O:Ê=KCFØ<A§ã���ÝJ? â Ø�EFEGØ_×�CFAJ�·ÜJ;@Ø�ܹØ\ÛÙ@Ch=KCFØ<A"?�AJÙ>�J;@?IÙD=KÝJ:\=�=KÝJ? â �JAMßI=KCGØ�AJÙ�CFA �Yê �"%�:<;>?gCFAJLJ?I?�L'×q?IEFEoÛ�LJ?7èOAJ?�L�Ø�H��>?IßI=@Ù�ã���$% ��% �"$ �%&� '� D$<�.b5S5?7:9s;[<=*#2$465 � � ��WCDb5FAC<=*+5 �TD3Q _ n!]TDB4j<=]&DbOZ2�IKI�2���*+4CE ]T2$I#Q�5�<=@87 D��

)+*-, n!]TD d3AI 7 DbOX7:4T0�<=*�2�465 ;8( � $ �����������!� Q6D �64TD8Qa@\D80�7:@�5S* d$DFImG WVG ) ���$,UA�@VD ��DBIKI �XQ6D �64TD3QA�4TQa082�4T<�*K4&7 2 7�5 _ � O & *K5sWC2 7:4TQ6D3Q � 5V2�*K5bD\A�0^] ;H(C_

)K*+*-,��MA�0^] ;8( � i �\� ( = % *+5e5?<=@S*�0�<=ImG�*K4T0F@VD\A�5�*+4CEfA�4TQJ5?<�@�*�0�<=I G�082�4T0VA d$DHOZ2$@ A�I+I � ( = %�� ( _)+*K*K*m,R.�<�DVA 0^]q58< AE D $ � ê��������5�!�s�'ê <=]TDM5\2$I 76<�*�2$4C5h<X2s<�]TDP9fAD� *K9q*��?AC<=*#2$4b;T@V2 W�I#DB9 ) ����,r0VA4

WCDP@VD�;l@VDF5VDB4&<�D8Q�W3GqAh;�A�*+@P2$O�032$4&<=*K4&7 2�7:5[OX7:4T0�<=*#2$465 ��N � ( �!W �( %qÚ .:� �� (�� . V � ( �TY � V�SU_

���$%�%�� ��;@Ø<Ü ?I;>=KCG?�Ù ��C %Æ:<AJL �vCGC %�:<;@?�Ø�HeáVCGØ��JÙ>EGÖ�=K;@�M? â Ø�; $ � ��ã6BÆ?�AJßI?$:<Ù@Ù>�JàË? HeÖ�×�:�Ö�Ø âCFAJLM�JßI=@CFØ�A$=KÝO:Ê=�=@ÝJ?�;>?D?.&VCFÙ>=@Ù $#% �rê��������&�!�Q�#ê�"0Ù@�JßTÝ3=@ÝO:\= ;8( G = Ù@:\=KCGÙ>èO?IÙRÜM;@Ø�ܹ?�;t=KCF?IÙ ��C %k:<AML�vCGC %7ã·� ?$Ù@ÝMØd× =KÝO:\=g=@ÝJCFÙ1CGàËÜJEGCF?IÙD=KÝM?ÈÜM;@Ø�ܹ?�;t=KCF?IÙ �vC %0:\AJL �vCFC % â Ø�;0=@ÝJ? â �JAJßI=@CFØ�A�;8(':<AJL#=KÝJ?Ù@Ø�EG�M=KCGØ�A3=@ØÈÜM;@Ø�HJEG?�à �tê �4%qÙK:\=@CFÙ>èJ?�Ù �vCGCFC %7ã ��ÝJ?1èO;@Ùt=�ÜO:<;>=�Ø â =@ÝJ?gÜJ;@Ø}Ø â ß�Ø_á<?�;@Ù�=@ÝJ?1ß�:<Ù>?1×�ÝJ?�;>?- Ù>Ù@�JàÈÜM=KCGØ�A ��C %6CGÙ�Ù@:\=KCGÙ>èO?IL :<AJL«=KÝM?+�M=KCGEFCh=�Ö â �JAJßI=@CFØ�A�& CGÙ�H¹Ø��JAJLJ?IL§ã ��ÝJ?"Ù@?Iß�Ø�AML ÜJ:<;>=?'&}=K?IAJLJÙ0=@ÝJ? :<;>���JàÈ?�Ae=|=@Ø":<A��JArH¹Ø��JAJLM?�L��M=@CFEFCh=�Ö â �JAJß7=KCGØ�A�HeÖ�:\Ù@Ù@�MàËCGAJ�3=KÝJ:\=D=@ÝJ?ÉàÈ?�:<Ù>�J;@?� Ù@:\=KCGÙ>èO?IÙ - Ù@Ù>�JàÈÜM=KCGØ�A 6��CFC %ã��ÝJ?�èO;@Ùt=�CFAJLJ�MßI=KCGØ�A ÝeÖ}Ü Ø<=@ÝJ?�Ù>CFÙ�CFÙk=@ÝO:\= ;8( G = CFÙk×R?�EGEhÛ�LM?IèOAJ?IL§Þrß�Ø�Ae=@CFAr�JØ��JÙIÞ}:<AJL$H Ø<�JAJLJ?IL3:<AML;H( G = � i �\� ( G == %qÚ .L� �� ( G = � .:�&Y F CGÙqÙt=K;@CGßI=@EGÖÈCFAJßI;@?�:<Ù@CGAJ� :<AJL"Ùt=K;>CFßI=@EGÖÈß�Ø<AJß�:�á�? â Ø<;�?�:<ßTÝ+è &M?IL� ( G == % � ( G = ãÉ��?ÈÙ>ÝJØ_×ÇHeÖ#CFAMLJ�JßI=@CFØ�A�=@ÝO:\=1=@ÝJCFÙ1CGàËÜJEGCF?IÙD=KÝJ:\=1=KÝJ?$ßIEÑ:<CGà ÝJØ<EFLJÙ â Ø�; ;8(':<AML=KÝJ?1Ù>Ø�EF�V=KCFØ<A+:\=�Ùt=T:<�<? $ ã��cØ ?�AJÝO:\AJß�?1;>?�:<LO:\HJCFEGCG=�Ö$=KÝJ?|;@?�àË:<CGAJLJ?�;qØ â =KÝJCGÙ�ÜJ;>ØVØ â CGÙ�Ø�;>�e:<AJCG��?�LCFA"èJá<?·Ùt=K?�ÜMÙ�ã� "?�#� ' qåa?7=M� ( = %�� ( :<AML f (a)*� ���(1H¹?�:<;@HJCh=K;@:<;>Ö6HJ�M=%è &V?�L§ã 9ÆØ<=K?q=@ÝO:\=k=@ÝJ?�Ù@?7=�� (�� f (��A6�($%LJ?IèJAJ?�L�:<ÙÆ:<H Ø_á<?6CGÙ�AJØ�AVÛÐ?�àÈÜM=�Ö"Ù>CFAJßI? f (�)*� ���(Mã�/OØ�;�?�:\ßTÝ ��Ny�!W"% % � ( � f (`�A68("%qLJ?7èOAJ?

* ( ��Ny�!W��\� ( = %�ÚT�:& �=N % - ( 3 5 ;8( G = � � �@W �\���\�'�( G = � �1,($% �\� ( = �B� � � ( G = �=�(= �!I �D% �Yê $%

:<AJL"AJØ\=K?|=@ÝO:\=�=@ÝJ?1CFAe=K?I��;K:\E CGA �tê "%RCFÙRCFAJLJ?I?�L"×R?�EFEoÛ�LJ?7èOAJ?IL"Ù@CFAMß�? â Ø�;�:<EFE �=N �!W$% % � ( � f ( �A68(4%7Ú� �@W��\���l�'�( G = � �1,("%�� �'�( G = - �1,(�[�-*]4� �|) �'�( G = � �1,( ���(s� � ���( G = â Ø�;Ë?�:<ßTÝ(� % � ã

ê<ê

Page 13: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

9�Ø�;>?�Ø_á�?I;�Þ - Ù>Ù@�JàÈÜM=KCGØ�AJÙ �+:<AML � �vC %�=KØ���?7=KÝJ?I;|×�CG=@Ý�=KÝJ? CGAJLJ�Jß7=KCGØ�A�ÝeÖVܹØ<=@ÝJ?�Ù>CFÙ1CFàÈÜJEhÖ�=@ÝO:\=* (�CGÙgß�Ø�Ae=KCGAr�JØ��JÙ�:<AJL H¹Ø��JAMLJ?�L§ã �VCFAJßI?v6�(�� 3�=@ÝJ?ÈÙ@?I= � (�� f ( �@68($%1CFÙgßIØ�àËÜJ:<ßI=6CFàÈÜJEhÖVCGAJ�=KÝO:Ê=Æ=@ÝJ?gà3:D&MCGàËCG��:\=@CFØ�AÈÜJ;>Ø�HJEF?Ià

à3:D&;�� �M? � � -��

� * ( �=N �!W �\� ( = % BBB ��Ny�!W"% % � (�� f ( �A68(4%�� �Yê �A%

Ü Ø<Ù@Ù@?IÙ@Ù>?�Ù0:$Ù@Ø<EF�M=@CFØ�A ��N � ��W � %7ã� "?�#���§Ú%� ?|Ù@ÝJØ_× =KÝO:\=R=KÝJ?1Ù>Ø�EF�V=KCFØ<AË=KØ �tê �A%,CFÙR�JAJC,+r�J?\ã ��Ø�=@ÝJCFÙq?�AJL§ÞMAJØ<=K?Æ=KÝO:Ê= � (�� f (��A6�($%CFÙ'ß�Ø<Ará<?'& ÞgÝJ?�AMß�? CG='Ù@���ËßI?�Ù�=KØ Ù@ÝJØ_×-=@ÝO:\="=KÝM?�àË:<Ü * ( � i �\� ( = %+CFÙ'Ù>=@;@CFß7=KEhÖÍß�Ø<AJß�:�á�?\ã5åa?I=�=N �!W %&�D��N �!W % % � (�� f ( �A68(4%ÞE��N �!W % �� ��N �!W %3:<AJL�� % 1,3���ê .�H¹?�:<;@HMCG=K;@:<;>Ö :<AML LJ?IèOAM?�=Nl�!W��%�ÚC��� ��N �!W� % - �têa� � % �=N ��W� %ãÍ� ?�Ù@ÝJØ_× =KÝJ:\= * ( �=Nl�!W�\�\� ( = %���� * ( �=N �!W� �\� ( = % -�tê��� % * ( ��N �!W �\� ( = %ã < â W � W Þ0=KÝJCGÙ"CFÙ"=K;>CGá}CÑ:\EFEGÖ Ù@:\=KCGÙ>èO?IL§Þ â Ø�;"CFA =KÝMCFÙ"ß�:\Ù@?oN �� N :<AJL =KÝJ?Ë:<Ù@Ù>?�;t=KCFØ<A â Ø�EGEFØ_×�ÙgCFàÈàË?ILJCÑ:\=@?�EhÖ â ;>Ø�à-=KÝM?ËÙt=K;@CGßI=·ß�Ø�AMß�:�á}CG=�Ö#Ø â &Ïã�}Ø�:<Ù>Ù@�JàÈ?Ë=@ÝO:\=W �� W ã ��ÝJ? AMØ�AVÛ�;>?�LJ�MAJLO:<AJß7Ö�ß�Ø<AJLJCG=@CFØ�A �vCFC % â ;>Ø�à - Ù@Ù>�JàËÜV=KCFØ<A �"CGàËÜMEFCF?IÙÆ=@ÝO:\=0=@ÝJ?$àË?�:ÊÛÙ@�J;@:<HJEG?"Ù@?I= ( �KW� �!W� %'ÚT� �l� % ��� � �@W�T�\���\�'�( G = � �1,("% �� � �KW� �\���l�'�( G = � �1,("% � % � � � %DÝO:<ÙÜ Ø<Ù@CG=@CGá<?DàÈ?�:<Ù>�J;@?\ÞVC�ã{?\ãGÞ � ( G = �=�

(= � ( �KW �!W %)%e�;3Vã���ÝJ?|EGCFAJ?�:<;@Ch=�ÖÉØ â � � i � i ���'�( G = � �1,("%,CGàËÜMEFCF?IÙ

� �@W�l�\���l�'�( G = � �1,("%,��� � �@W� �\���\�'�( G = � �1,(4%�- �Yê���� % � �KW� �B�l�l�'�( G = � �1 ($% â Ø<;1:<EFE�� % � ã=��ÝJCFÙ=KØ��<?I=KÝM?�;�×�CG=@Ý'=@ÝJ?gÙ>=@;@CFß7=�ß�Ø�AMß�:�á}CG=�Ö'Ø â =KÝJ? â �JAMßI=KCGØ�A ;H( G = � i �\� ( G == %q�<CGá�?IÙ

;8( G = � � �@W�l�\���l�'�( G = � �1,("%&�B� ( = �\�D% ) � ;8( G = � � �@W �\���\�'�( G = � �1,("%&�\� ( = �\�D%- �tê���� % ;8( G = � � �@W �\���\�'�( G = � �1,("%&�\� ( = �\�D% �YêD#"%

â Ø�;�:<EGE�� %�� ×�ÝJ?I;@?�:\ÙÆ=@ÝJ?gCFAJ? +}�J:<EFCh=�Ö3CGÙ�Ù>=K;>CFß7= â Ø�; � % (8�KW� �!W� %7ã - EFÙ@Ø AMØ<=K?1=KÝJ:\=�=KÝJ?gÙt=K;@CGßI=ß�Ø�AMß�:�á}CG=�Ö+Ø â &�CGàËÜMEFCF?IÙ�=@ÝO:\= & ��N�(%e)�� & �=N % -;�tê ��� % & �=N %ã�<�Ae=K?��<;K:\=@CFAJ�ÉH¹Ø<=@Ý"Ù@CFLM?�Ù�Ø â �YêD#"%:<AJL�:<ÜJÜJEhÖ}CFAJ�$åa?�àÈàË: 2 â ;>Ø�à - ÜJÜ ?IAJLJC &6C Ö}CG?�EFLMÙ�=KÝJ?gLJ?IÙ@CF;>?�L�CFAJ? +r�O:<EFCh=�Ö

* ( ��N�l��W���B� ( = % � & �=N(% - ( 3 5 ;8( G = � � �@W�l�\���l�'�( G = � �1,("%&�B� ( = �\�D% � ( G = �Z�(= �!I �(%

� ���)& �=N % - ( 3 5 ;8( G = � � �@W �\���\�'�( G = � �1,("%&�\� ( = �\�D% � ( G = �=�(= �!I �D%��

- �Yê ��� % � & ��N % - ( 3 5 ;8( G = � � �@W �\���\�'�( G = � �1,("%&�\� ( = �\�D% � ( G = �=�(= �!I �D% �

� � * ( ��N ��W �\� ( = % - �Yê ��� % * ( �=N ��W �\� ( = %&���ÝJCFÙ$;>?�Ù@�MEG=ÈÜ ?I;@àÈCG=@Ù �JÙÈ=@Ø�LM?IèOAJ?'=KÝM?�Ù>Ø�EF�V=KCFØ<A =@Ø =@ÝJ?'à3:D&MCGàËCG��:\=@CFØ�A�ÜJ;@Ø<HJEF?Ià �tê �$%É:<Ù3:â �JAJß7=KCFØ<A0��N � ( �!W �( %�Ú .:� ���(8�

. V � ( �TY � V�S0Þ

�=N � ( �!W �( % � f ( �\� ( = %�ÚT� :\;@�|àË:(&; � �E? � � -��

� * ( ��Ny�!W��\� ( = % BBB �=N �!W$% % � ( � f ( �A68(4% � � �Yê !$%

� "?�#� �§Ú ��?«ßIEÑ:<CGà =@ÝO:\=�=@ÝJ?«àË:<ÜJÜJCGAJ��Ù>N � ( ÞaW �( :<AJL =KÝM? â �JAJßI=@CFØ�A ;8( :<;@?çßIØ�Ae=KCFAr�JØ<�JÙ�ã��Ø Ù>?�?�=KÝJCGÙ�ÞÆLJ?IèJAJ?�=KÝJ?�HJ�MLJ��?I=�Ù>?I= â Ø�;':<Eh=K?I;@AO:\=@CGá<? � f (`�A68("%+:<Ù':«ßIØ�;@;>?�Ù@ܹØ�AJLM?�AJßI? � ( Ú

ê �

Page 14: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

.:� ���(8� . V F BGHG�� � V�S0ÞR×�ÝMCFßTÝ CFÙËAJØ�AVÛÐ?�àÈÜM=�ÖeÛTÞ�ß�Ø�àÈÜO:<ß7=>Û :<AJL ß�Ø<Ará<?'&rÛÐá\:<EG�J?�L Ø�A Ch=KÙ

LJØ�àË:<CFA�Ø â LJ?7èOAJCG=@CFØ�Ayã*/O�J;t=KÝJ?I;@àÈØ�;@?\Þ%×q?"Ù>ÝJØ_× CFAçåa?�àÈàË:�ê 3�CFA - ÜJÜ ?IAJLJC & C =@ÝO:\= � ( CFÙß�Ø�Ae=@CFAr�JØ��JÙIã ��ÝJCFÙ�=@Ø���?I=@ÝJ?�;�×�Ch=KÝ"=KÝM?1ß�Ø�Ae=KCGAr�JCG=�Ö3Ø â =KÝJ? â �JAMßI=KCGØ�A * ( CFàÈÜJEFCG?�Ù,=KÝJ?1ßIØ�Ae=KCGA}�MCG=�ÖØ â =@ÝJ?ÆÙ@Ø�EG�M=KCGØ�A â �JAJßI=@CFØ�AJN � ( :\AJL0W �( HeÖ$á}CF;>=@�J?�Ø â =@ÝJ? ��ÝJ?�Ø�;>?�à Ø â =KÝJ?|9�:(&VCFà��Jà �vß â ã �}=KØ"�\?IÖ� åa�Jß�:\Ù·ê_ì<ì �JÞOܧã #"2$:<AJL�Üyã !��4%7ã=�}�JHJÙ>=@CG=@�M=KCGAJ� =KÝJ?6Ù@Ø�EG�M=KCGØ�A1�tê !"%�CGAe=KØ �tê �$%�Ö}CG?�EFLMÙ�=@ÝJ?gá<:\EF�J?â �JAJß7=KCFØ<A�LM?IèOAJ?IL â Ø�;�:\EFE f (7)*� ���(È:<AJL>� ( = %>� ( :<Ù;H( � f ( �\� ( = %�� * ( ��N � ( � f ( �\� ( = % �!W �( � f (`�\� ( = %��\� ( = %<� �YêD2"%

=KÝJ?gßIØ�Ae=KCFAr�JCh=�Ö"Ø â ×�ÝJCFßTÝ â Ø�EGEFØ_×�Ù�CFàÈàÈ?�LJCF:\=K?IEGÖ â ;@Ø�à =KÝJ?gßIØ�Ae=KCFAr�JCh=�Ö"Ø â * (È:<AJLaN � ( Þ W �( ã� "?�#� � «��?�Ù>ÝJØ_× =@ÝO:\=�;H( � i �\� ( = %$CFÙÈÙ>=@;@CFß7=KEhÖ ßIØ�AJß�:_á<?<ã �cØ =KÝMCFÙ3?IAJL§Þ�EF?7= f �:<AML f qH ?:<;@HMCG=K;@:<;>Ö Ù>�JßTÝ =KÝO:Ê= f J) � ���(JÞ f c) � ���(ç:\AJL f �� f Ñã /%C & � % 1,3���ê�.,:<AJL LJ?IèOAM?f �ÚT� � f `- �têj� � % f Fã/O�J;t=KÝJ?I;@àÈØ�;@?\Þ�EG?I=?�=N � �!W� � %$ÚT� ��N � �!W � %�� f �B� ( = % % � (�� f �@68($%1:<AML�=N � �!W� � %1ÚC� ��N � �!W � %�� f �\� ( = % % � (�� f �@68($%ÆH ?É=@ÝJ? Ø�ÜM=@CFàË:<EÏÙ@Ø�EG�M=KCGØ�AJÙ0H¹?�EGØ�AJ��CGAJ�Ë=@Ø f Ï:<AMLf �:<AML�EG?I= �=N � �!W � %·ÚT� � �=N � �!W� � %�- �tê�� � %���N � �!W� � %0H ? =KÝM?�CF;gßIØ�Aeá�?'&�ßIØ�àÉHJCGAO:\=KCGØ�A§ã 9ÆØ<=K?=KÝO:Ê= �=N � �!W � % % � (�� f l�@68(4%|HJ�M=6Ü Ø<Ù@Ù@CGHJEGÖ �=N � �!W � % �� ��N � ��W � %�� f l�\� ( = %ÞaC±ã ?<ãhÞ��=N � �!W � %|LJØ}?�ÙgAJØ<=ÝO:�á�?+=@Ø�H ?3=@ÝJ?+Ø�ÜV=KCFàË:<E,Ù@Ø<EF�M=@CFØ�A :\= f eã - EGÙ@Ø�AMØ<=K? â ;>Ø�à =KÝJ?+HM�JLJ��?7= Ù@?7= =KÝO:\= f �� f CFàÈÜJEFCG?�Ù0=@ÝO:\=��=N � �!W� � % �� �=N � �!W� � %ã��ÝJCFÙg=KØ��<?I=KÝM?�;·×�Ch=KÝ �têD2"%g:<AJL =KÝJ?ËÙ>=@;@CFß7=�ßIØ�AJß�:_á}Ch=�Ö�Ø â=KÝJ? â �JAMßI=KCGØ�A * ( � i �\� ( = %R=KÝJ?I;@? â Ø<;@?gCFàÈÜJEFCG?�Ù�=KÝJ?gLJ?IÙ@CF;>?�L�CFAJ? +}�J:<EFCh=�Ö

;H( � f l�B� ( = % ) * ( �=N � �!W � �\� ( = %<�� * ( � � �=N � �!W � % - �Yê ��� %���N � �!W � % �\� ( = %� � * ( ��N � �!W � �B� ( = % - �Yê ��� % * (=�=N � �!W � �\� ( = %� � ;8( � f �\� ( = % - �tê ��� % ;8( � f �\� ( = %&�� "?�#��� ��? :\;@?#EF? â =�=@Ø Ù>ÝJØ_× =KÝO:Ê= ;8( � i �B� ( = %+CFÙ�Ù>=@;@CGßI=KEhÖÍCGAJß�;>?�:<Ù>CFAJ�Jã ��Ø =KÝJCGÙ'?�AJL§Þ1EG?I=f � f ) � ���(+H¹?$:<;@HMCG=K;@:<;>Ö<ã6åÏ?7=��=N � �!W� � %|:<AJL ��N � �!W� � %|H ?ÉLM?IèOAJ?IL :\Ù1CFA�=@ÝJ? ÜJ;@?7á}CFØ��JÙÙ>=@?�ÜÈ:<AJLÉÙ>?I=���ÚT� f � f �;30:\AJL6�=N � � �!W �� %qÚT� ��N � -����!W � %7ã 9DØ<=@?q=KÝO:Ê= �=N � � �!W �� % % � (�� f �A6�($%HJ�M=ÆܹØ�Ù@Ù>CFHJEhÖ �=N � �!W� � % �� �=N � � �!W �� %7ã,BD?IAJß�?\Þ�?'&VÜJEFØ<CG=KCGAJ�É=KÝM?6Ùt=K;>CFßI=�àÈØ�AJØ\=KØ�AJCGß�Ch=�Ö3Ø â &ÏÚ

;8( � f �\� ( = % ) * ( ��N � � �!W �� �\� ( = %�� * ( �=N � -����!W � �B� ( = %� * ( ��N � �!W � �B� ( = %�� ;8( � f �\� ( = %&�æqØ�AJÙ>CFLJ?I;ÉAJØ_× =@ÝJ?+Ù>?�ß�Ø<AJL ß�:<Ù>?+×�ÝJ?�;>?�& CGÙÉAJØ<=�AJ?�ßI?�Ù>ÙK:<;>CFEGÖ H Ø<�JAJLJ?ILçHJ�M= � ÙK:Ê=KCFÙtèO?�Ù - ÙtÛÙ@�JàÈÜM=@CFØ�A E�vCFC %7ã���ÝJ?�ÜJ;>?Iá}CFØ<�JÙkCFAMLJ�JßI=@CFØ�A·ÜJ;@Ø}Ø â àË:�Ö6=@ÝJ?�A H¹?�;>?�ܹ?�:\=@?�L �JAJLM?�;%=@ÝJ?�CFAMLJ�JßI=@CFØ�AÝeÖVܹØ<=@ÝJ?�Ù>CFÙ%=@ÝO:\= ;8( G = CGÙc×R?�EGEhÛÐLJ?IèOAM?�L$:<AJL�ß�Ø�Ae=KCGAr�JØ��JÙ�:\AJL ;8( G = � i �\� ( G == %qÚ .:� �� ( G = � .L�&Y FCFÙ�Ùt=K;@CGßI=@EGÖ·CFAJßI;@?�:\Ù@CFAM�g:<AJL$Ù>=@;@CFß7=KEhÖÉß�Ø<AJß�:�á�? â Ø�;�?�:<ßTÝf� ( G == %>� ( G = ã�/O;>Ø�à åa?IàËàË:1ì1CG= â Ø�EGEFØ_×�Ù=KÝO:Ê= â Ø�;Æ?�:<ßTÝc� ( = %j� ( =KÝJ?·àË?�:<Ù@�M;@? � ( G = �=�

(= � i %�CFÙ|Ù>�JÜJܹØ�;>=@?�L�Ø<A�:ËÙ>�JHJÙ@?7=1Ø â =@ÝJ?�ßIØ�àËÜJ:<ßI=

Ù@?7= �� ( G = ã@/O;@Ø�à/åa?�àÈà3:�>+:<AML�=KÝJ? /O?�EFEG?�;YÛ�ÜJ;>Ø�Ü ?I;>=�Ö'Ø â � ( G = CG=Æ=KÝJ?IA â Ø�EFEGØd×�Ù�=@ÝO:\= â Ø<;D?�:<ßTÝ�=N �!W$% % � (�� f (`�A68("%�:<AJL>� ( = %>� ( =KÝJ? â �JAJß7=KCGØ�A

* ( �=N �!W �\� ( = %�ÚT�+& �=N %_- ( 3 5 �� � ;H( G = � � �KW��\���l�'�( G = � �1,("%&�\� ( = �\� � � ( G = �Z�(= �!I �(% �Yê >$%

ê

Page 15: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

CFÙ�×q?IEFEhÛÐLJ?IèJAJ?�L ��C±ã ?<ãhÞ * ( ��Ny��W �\� ( = % d� %R:<AJL"ßIØ�Ae=KCGA}�MØ��JÙ�ã � ?�ܹ?�:Ê=KCFAM�ÉÙ>=@?�ÜJÙ1êIÛ #·Ø â =@ÝJ?0ÜJ;>?Iá}ChÛØ��JÙÆ:<;>���JàÈ?�Ae=�=KÝJ?IA�Ù>ÝJØ_×�ÙÆ=@ÝJ?gß�EÑ:\CFà�ã �

5Æ=@CFEFCG��CGAJ��=KÝJ?�á<:\EF�J? â �JAJßI=@CFØ�A ; = Ø�HM=T:\CFAJ?ILÉCFA6=KÝJ?�èOAO:<EV;@?�ßI�J;@Ù>CFØ�A�Ù>=K?IܧÞ�ßIØ�AJÙ@CGLJ?�;�=KÝJ? â Ø�EFEGØd×�CGAJ�Ø�AJ?Û�Ù>=K:<��?gLJ?Iß�CFÙ>CFØ�A'ÜJ;>Ø�HJEG?�à LM?IèOAJ?IL â Ø�;�:\EFE �K1a�A6 % � 3Ë:<AML f � ��� b��Z1ÉÚ

àË:(&;�� �M? � � -��

� & �=N %_- ( 3 5 ; = � � �KW��\���`�' = �!1F% �\�D% � = �KI �(% BBB N�-h[�-�] D 6�� f ��[�)*���� b ��1 ��� �Yê_ì$%

��ÝJ? â Ø<EFEFØ_×�CGAJ��=KÝJ?IØ�;@?Ià&Ù>ÝJØ_×�Ù�=@ÝO:\=c=KÝJ?RÙ@Ø�EG�M=KCGØ�A1=KØ �Yê_ì$%aCFÙÏ�JAJC�+r�J?�:<AML�ß�:\AÉH ?��JÙ>?�L�=@Ø���?I=@ÝJ?�;×�CG=@Ý'=@ÝJ? â �JAJß7=KCFØ<AJÙ�LJ?IèOAM?�L�HeÖ �Yê !$%R=@ØËßIØ�AJÙ>=@;@�Jß7=D:<A�Ø<ÜM=KCGà3:<E¹Ù>=@;K:\=@?��<Ö<ã��� ��%��$��� '� 4TQCDB@k<=]&DM] G ;[2 <=]&DB5VDF5k2�O���@\2V;�2�5�* <�*�2$4��kI#D$<�<=]TDMOX7:4&0$<=*#2$465 ��N � ( �!W �( %�� $ � ê������������ W6DeQCD��64TD3QA�5 *K4R) ���3, ��]TDB@\D N � � � f � �\� � = %qÚT� f � A�4TQ W �� �Z� � = %�ÚT� 3 ��

�= %�� � _ n!]TDB4 OZ2$@[DVA 0^] �K1a�A6 % � 3

A�4TQ f � ���� b ��1 <=]TDpOZ2$I+I�2���*K4CE ]T2$I�Q 5�<=@?7�D��

)+*-, n!]TDh;l@V2 W�I�DF9 ) � �8, ] A�5pA�7:46* �67�Db5\2$I 7C<=*�2�4 �=N � b �!W �b % % � V�SH_)K*+*-, n!]TD 58<=@BA <XDFEG � L � � g � % Q6D �64TD3Q WVG <�]TD 2V;�<=*K9fA�I[Q6D30B*K5S*�2$4 �=N � b �!W �b % O�@\2$9 )K*-,�A�4TQJ;lI A�465

�=N � ( �!W �( %�Ú � ( �TY � V�S � $ ��ê��������5�!� Q6D��C4TD8Q @VD80�7:@�5S* d�DBImG/A�5�

N � ( �Z� ( = % ÚT� N � ( � � �KW �(ZY = �Z�(ZY == % �\��(`�`�'�(�� �1,(ZY = % �\�

(= %W �( �=� ( = % ÚT� W �( � � �@W �(ZY = �Z�

(yY == %&�\��( �\�'�( � �1,(ZY = %&�\�(= %

*K5 A4 2V;�<=*K9fA�I&5?<�@BAC<�DFE�Ga*+4x<=]TDp5VDF465VDs2$O sD��646*Z<=*#2$4 � _

)+*K*K*m, l2$@ A�4:Ga58<=@BA <XDFEG � L � g % %B�@1a�A6 � f % �

�=N b��!W�b'% �� �=N � b �!W �b % ,>- .0* b(� L � i %21 d ,�- .0* b(� L � � i %21����ÝJ?+ÜJ;>ØVØ â Ø â ��ÝJ?IØ�;@?Ià êËß�:<A«H¹? â Ø<�JAJL«CGA �V?IßI=KCGØ�A - ã �CGA - ÜJÜ ?IAJLJC & - Ø â =KÝMCFÙ6ßTÝO:<ÜM=@?�;�ã<Ð=Ë:<Ù@Ù>?�;>=@ÙË=@ÝO:\=Ë:<A Ø�ÜM=KCGà3:\EqÙ>=@;K:\=@?��<Ö ?.&VCFÙ>=@ÙÈ:<AJL ß�:<A H ?'ß�Ø<AJÙ>=@;@�Jß7=K?�L â ;@Ø�à =@ÝJ?'Ù@Ø�EG�M=KCGØ�AJÙØ�HM=K:<CFAJ?IL â ;@Ø�à =KÝJ?1;>?�ß��M;@Ù@Chá�?6LJ?IèJAJCG=@CFØ�A �Yê �"%7ã�9�Ø�;@?gCFàÈܹØ�;>=K:<Ae=KEGÖ<ÞVÝMØd×R?Iá<?�;IÞ¹Ch=�?�AMÙ@�J;>?�ÙD=@ÝO:\==KÝJ?�Ø<ÜM=KCGà3:<EÆLJ?Iß�CFÙ>CFØ�A â Ø�; ��� 3«CFÙ+�JAMC,+r�J?�EhÖÍLJ?7èOAJ?IL HeÖÍ=@ÝJ?�Ù@Ø�EG�M=KCGØ�AÍ=KØ«=@ÝJ?�Ø�AJ?Û�Ùt=T:<��?ÜJ;@Ø<HJEF?Ià �tê_ì"%7ã�/OØ�;,:<Eh=K?I;@AO:\=@CGá<?ÆÜM;@CFßI?�Ù �@1a�@6 %�:<AJLË×R?�:\EG=KÝ f LJ?I=@?�;>àËCGAJ?�LÈHeÖ �têD%%=KÝMCFÙ,Ø�ÜM=@CFàË:<ELJ?�ßICFÙ>CFØ�A+LM?IèOAJ?IÙq=KÝM?0LJ?�àË:<AJL3H ?IÝO:�áVCGØ�;qØ â =KÝJ?|ß�Ø�AJÙ>�JàÈ?�;qCGA3=KÝM?|LJ?Iß�CFÙ>CFØ�A3Ü ?I;@CFØ}L§ã ��ÝJ?0àË:<CFA;@?IÙ@�JEh=DØ â =@ÝJCFÙ�Ù>?�ßI=@CFØ�A�CFÙ�Ù>�JàÈà3:<;>CF�I?�L"CFA"=@ÝJ? â Ø�EFEGØd×�CGAJ��=@ÝJ?�Ø�;>?�à�ã��� ��%��$��� �� D$< <=]TDq082$4C5?7:9�DB@�� 5b;lI�A�4C46*K4CEa]T2�@�*��$2$4 � � ê A�4&Q`D �:;[D80�< AC<�*�2$465 �'�� ���' = ���������l�'�� % %�F �G ��1 � � �1 = ��������� �1z��Y = % %XF ��Y =GHG A�4&Q � % �,;>Ø�H � � � % WCDUE *Zd$DF4xA�4TQRI#D$<i.p5�587:9�;�<=*�2�465 � � �/W6D� ; W #&.�Y-Q[!=4&E�*�4&0I# 0[(:48*b} ! Q !/0 ������ y������ ��� yy � c������� (+E�� � k-\

ê�

Page 16: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

5BAC<�*K5 �TD8Q _ n!]TDB4 <�]TDB@\D�D � *K58<=5JAx082$4&<�*K4&7 2 7:5fQCDB9fA�4TQxOX7:4T0�<=*#2$4�� � i � � �l�'�� �1 % Q6D��C4TD8Q`OZ2$@ AIKI�@1a�A68% � 3 A�4TQ f )*��� b���1 A�5

� �@1a�@6 � f � � ���'Z� �1F% ����� � �K1a�A6 � f � � ���'Z� �1 %��� �@1a�A6_� f � � �l�'�� �1F%��� �K1a�A6 � f � � ���'y� �1F%

�� ���43$%

ÚT� :<;>�Ïà3:(&; � � � ?� � - � -��

� & �=N % - ( 3 5 ; = � � �K[ �^] �\�����' = � 1F% �\�D% � = �KI �(% BBB N�-2[j-2] D 63� f ��[ )*��� b ��1 � �

���$%�%�� ä &VCFÙ>=@?�AJßI?#Ø â =KÝJ?�LJ?Ià3:\AJL â �JAJßI=@CFØ�A â Ø<EFEFØ_×�ÙËCFàÈàË?ILJCÑ:\=@?�EhÖ â ;@Ø�à ��ÝJ?IØ�;@?Ià ê �vC %7ãæqØ�Ae=KCGA}�MCG=�Öµß�:<A�H ? ÜJ;>Ødá<?�L :<Ù#CFAµÙt=K?�Ü CFA =KÝM? ÜM;@Ø}Ø â Ø â ��;>Ø�Ü Ø<Ù@CG=@CFØ�A�ê<ã <�A&=@ÝJCFÙ�;>?7Û�e:<;>L§Þ�ß�Ø�Ae=@CFAr�JCG=�Ö�Ø â =@ÝJ?+HJ�JLM��?I= ßIØ�;@;>?�Ù>Ü Ø�AMLJ?�AJßI?1�@1a�A6 � f % � b �@1a�A6_� f %$ÚC� � �=N ��[ �M] % %� V#P V#R � Nz- [c-�] D 6 � f ��[#) ���� b ��1c" â Ø�EFEGØ_×�Ù0HeÖ#:<ÜJÜJEhÖ}CFAJ�'åa?�àÈàË:�ê 3MÞaAJØ\=KCFAM�'=@ÝO:\=� b��@1a�A6 � f % �Q� ��Ny�^[ �^] % % � VNP VNR � N�-2[�-�] D 63�U1 f ��[0)*���� b�" â Ø�;�?�:<ßTÝ 1 � 3Mã �

��ÝJ? â �JAJßI=@CFØ�A � � i � � �l�'�� �1F%kLJ?�Ù>ß�;>CFH¹?�Ù,=KÝJ?Æß�Ø�AMÙ@�JàÈ?�; {Ù�Ø�ÜM=@CFàË:<EMßIØ�AJÙ@�MàËÜM=@CFØ�AË:<AJLÈCFAeá<?�Ù>=@àË?IAe=CFA�H¹Ø�AJLJÙg:\AJL�Ù>=@ØVß��rÙgCFA�=@ÝJ? LJ?�ßICFÙ>CFØ�A�ܹ?�;>CFØ}L�� � 3 â Ø�;1:<Eh=K?�;>AO:\=@CGá�?·ÜJ;@CGß�?IÙ��@1a�A6 % � 3":<AML×q?�:<EG=@Ý f )*���� b���1 LJ?I=@?�;@àÈCFAM?�L6HrÖ?�YêD%7ã - =Ï=KÝJCGÙcܹØ�CGAr=�Þ\Ù>Ø�àÈ?�;>?�àË:<;)�rÙ�:<H¹Ø��M=Ï=KÝJ?,ßIØ�AJÙ@�MàË?I; Ù×q?�:<EG=@Ý f :<AML =KÝJ?3ß�Ø�AJLMCG=KCGØ�A f ).��� b���1 :<;@?3CFA«Ø�;>LJ?�;6×�ÝJCFßTÝ«×q:<Ù ;>?�+r�JCF;>?�L«=@Ø�Ø�HM=K:<CFAç:AJØ�AVÛÐ?�àÈÜM=�Ö"Ùt=K;K:Ê=K?��\Ö"Ù@?7=�ã�5DÙ>CFAJ�È?�+r�O:\=@CFØ�A1�YêD%R=KÝJCGÙ�ß�Ø�AMÙ>=K;@:<CFAe=Æß�:\A�H¹?0×�;@Ch=@=K?IA�:\Ù

'�b�-h1vY = [`Y = - �:6c-kIlb.% D ]_Y = )*���� b���1a� ���VêD%

�VCFAMß�?"HeÖ:� $% �� b ) 3VÞ�CG= CGÙÉß�EG?�:<;�=@ÝO:\=6���VêD%·ß�:<A Ø�AJEhÖ H¹?3á}CFØ�EF:\=K?ILçC â [\Y =�d 3VÞ�C±ã ?<ãhÞ�C â =KÝJ?ß�Ø�AMÙ@�JàÈ?�;'ÝO:<Ù'=T:��<?�A ß�;>?�LJCh='HrÖ Ù>?�EGEFCFAM�çH Ø�AMLJÙ'CFA =KÝJ?#ÜJ;>?Iá}CFØ<�JÙ�ܹ?�;>CFØ}L§ãÇ��? Ù>?�?#=KÝO:Ê=�:Ù@���ÈßICF?�Ae=�ß�Ø�AJLMCG=KCGØ�A â Ø�; � �VêD%|=@Ø�ÝJØ�EGL�CGÙ6=@ÝO:\=v[`Y = )��E�K'�b���1vY = - �� b�� �@1#1vY = %B%7ã"BÆØd×R?Iá<?�;IÞåa?�àÈà3: ê ÝO:<Ù�Ù@ÝJØ_×�A =@ÝO:\=�=KÝJ?I;@? ?'&VCFÙt=�EFØ_×q?I;�H¹Ø��JAMLJÙ�Ø<A =@ÝJ?�ßIØ�AJÙ>�JàË?I;@Ù�ß�;>?�LJCh=�=K:4�rCFAJ�H ?IÝO:�á}CFØ�;k×�ÝJCGßTÝ3:\;@?�LJ?7=K?�;>àËCGAJ?�L$HeÖÉ=@ÝJ?�?'&Vܹ?�ßI=K:\=KCGØ�AJÙ â Ø�;kÝMCFÙ�LJCGÙ@ß�Ø<�JAe=K?�L â �M=@�J;@?�AJØ�A}Û�ß�:\ÜJCG=K:<ECFAJßIØ�àÈ?ËÙt=K;@?�:<à�ã�é1CGá�?IA =KÝM?�Ù@?"Ù>�JH��>?IßI=KChá�?"?.&Mܹ?�ß7=T:\=@CFØ�AMÙ·=KÝM?+ß�Ø�AMÙ@�JàÈ?�;·ßTÝJØVØ<Ù@?�Ù$:�Ù>=K;@:\=K?I�<Ö×�ÝJCFßTÝ ?IAJÙ@�J;>?�Ù$ÝJCGÙÉÙ@Ø�Ehá�?IAJßIÖ :Ê=$:<Aeܹ֫Ø�CFAe=�CFA«=KCGàË? â Ø�; :\ArÖ Ü Ø<Ù@Ù@CGHJEF?3;@?�:\EFCF��:\=KCGØ�A Ø â ÜJ;@CGß�?�Ù:<AJLÍLMCGá}CFLJ?IAJLJÙIã BÆ?�AJßI?�×R?�Ù@?I?�=KÝO:Ê=3C â LJ�J;>CFAJ� =KÝJ?�ÜJ;@?7á}CFØ��JÙ�t� �6ê�=@ÝJ?�ßIØ�AJÙ@�MàË?I;3ÝO:<Ùß�Ø�;>;@?IßI=KEhÖ :<Ae=KCFßICFÜO:Ê=K?�L ÝJCFÙËAJØ�AVÛÐß�:<ÜMCG=T:\EÆCGAJß�Ø<àË? '�b':<AJL =@ÝJ?�H¹Ø�AJL ;@?I=@�J;@As1 � 3«:\=Ë=KCFàÈ?��� 3��v:<AJL$ß�Ø�Ae=@CFAr�J?�Ù,=KØgÝJØ<EFL =KÝJ?�Ù@:<àË?�?.&Mܹ?�ß7=T:\=@CFØ�AMÙ â Ø<;�ÝJCFÙ�LJCGÙ@ßIØ��JAe=K?IL â �M=@�J;@?�AJØ�A}Û�ß�:\ÜJCG=K:<ECFAJßIØ�àÈ?DÙt=K;@?�:<à?%7Þr=KÝJ?0CGAJ?�+r�O:\EFCG=�Ö�[\Y = )*�E�K'�b���1vY = -|�� b�� �@1O1vY = %)%,CFÙR:<�M=@Ø�à3:Ê=KCFß�:<EFEhÖÉÙ@:\=KCGÙ>èO?IL:<ÙD:Ëß�Ø<AJÙ@? +}�M?�AJßI? Ø â =@ÝJ?�ßIØ�AJÙ@�MàË?I; Ù|ß�;>?�LJCh=D=K:4�rCFAJ�ÈH¹?�ÝO:�á}CFØ�;Iã <Ð=DCFÙ�=KÝJ?I;@? â Ø<;@?6ß�EF?�:<;�=KÝO:Ê=0:<ÙEFØ�AM��:<Ù6ß�Ø<AJÙ@�JàÈ?�;>ÙcÜJ;@?ILJCFß7=KCGØ�AJÙ â Ø�; â �M=K�J;>?3AJØ<AVÛ�ß�:<ÜJCG=K:<E�CFAMß�Ø�àÈ?È:<AJL â �V=K�J;>?ËH¹Ø�AJL�;@?I=@�J;@AMÙ:<;@?"ßIØ�;@;>?�ß7=$Ø�; :\= EG?�:<Ùt= Ù@���ËßICF?IAr=@EGÖ ÜJ;@?Iß�CFÙ>?<Þ�HO:<A �r;>�JÜM=Kß7ÖçCFÙ�?'&Vß�EG�JLJ?�L HeÖ«=@ÝJ?"H ?IÝO:�á}CFØ�;ÉØ âß�Ø�AMÙ@�JàÈ?�;>Ù�=@ÝJ?�àÈÙ@?IEGá<?�Ù�ãRæqEG?�:<;>EGÖ�ÞVC â ?'&Vܹ?�ß7=T:\=@CFØ�AJÙ â :<CGE¹=@Ø H ?1ßIØ�;@;>?�ß7=|:\AJL�:<ßI=@�O:<E§;>?�:<EGCF��:Ê=KCFØ<AJÙLJ?Iá}CF:\=K?|=@ØVØ·àÉ�JßTÝ â ;>Ø�à�=KÝJ?ICF;�ÜJ;@?ILJCFß7=K?�L+á\:<EG�J?�ÙIÞJ:�ܹØ<=@?�Ae=KCF:<E�ÜJ;@Ø�HMEF?�à Ø â HJ:<A �r;@�JÜV=KßIÖ3ß�Ø�àÈ?�ÙCFAe=KØ ÜJEF:�Ö ��×�ÝJCGßTÝ àË:�Ö Ù>=@CFEGE|H¹?�:�á<Ø�CFLJ?IL C â LMCGá}CFLJ?IAJL ÜO:�ÖVàÈ?�Ae=@Ù�:<AML87\Ø�;':<Ù>Ù@?7=�ÜJ;>CFßI?�Ù�:<;@?Ù@���ÈßICF?�Ae=@EGÖ"EF:<;@��? %7ã

ê #

Page 17: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

� � �� �E��� �X � �z�6������� � � � ������� *����� � ����ÝJ?�ÜM;@?Iá}CGØ��JÙÆÙ@?�ß7=KCGØ�A�ÝO:\ÙD?IÙ>=T:\HJEFCGÙ@ÝJ?IL�=KÝM?·?.&MCGÙ>=@?�AJßI?ÉØ â Ù>Ø�EF�V=KCFØ<A'=@ØË=@ÝJ?·ßIØ�AJÙ>�JàË?I; Ù|àÉ�MEG=KCoÛÜ ?I;@CGØVL LJ?Iß�CFÙ>CFØ�A ÜJ;>Ø�HJEF?Ià :<AJL Ø â : ßIØ�Ae=KCFAr�JØ<�JÙ�LM?�àË:<AJL â �JAJßI=@CFØ�AMÙ��JAMLJ?�;6+r�JCG=@? �<?�AJ?I;K:<E:<Ù@Ù>�JàÈÜM=KCGØ�AJÙÈØ�A =@ÝJ?�ßIØ�AJÙ>�JàË?I; Ù3ÜJ;>? â ?I;@?�AMß�?�ÙIã:��Ø�LJ?�;>CGá�?�:<LJLMCG=KCGØ�AO:<EqÜJ;@Ø�ܹ?�;t=KCG?�ÙÈØ â =@ÝJ?�Ù>?LJ?�àË:<AJL â �JAJß7=KCFØ<AÈ=@ÝJCFÙ,Ù@?IßI=@CFØ�A3:<Ù@Ù>�JàË?IÙ�:gÙ@ܹ?�ßICGèOß â �JAJßI=@CFØ�AJ:<E â Ø�;@à Ø â =KÝM?D�M=@CFEGCG=�Ö â �MAJßI=@CFØ�A=&CFA - Ù@Ù>�JàËÜV=KCFØ<A �È×�ÝJCFßTÝ�?.&VÝJCFHJCh=KÙ0ßIØ�AJÙt=T:<Ae=6:<HJÙ>Ø�EF�V=K?�;>CFÙB��:�á�?I;@Ù>CFØ�A ��æ � � - %ã�F�cØ+=KÝJCGÙ0?�AML×q?6àË:4�<?0=@ÝJ? â Ø�EFEGØd×�CGAJ� :<Ù>Ù@�JàÈÜM=@CFØ�A§ã��� ��� "$ �%&� �n!]TD 76<=*+IK* <-GfOX7:4&0$<=*#2$4 & *+4a.p5�587:9�;�<=*�2�4 � *K5b2�Or<�]TDpOZ2$@�9

& ��N � � % � ���� ê� N�� � �� 3

EFAkN � � 3��� �"%

æqØ�AJÙ>CFLJ?I;6=@ÝJ?$;@?�ßI�J;@Ù>CGá<?ËÙ>Ø�EF�M=@CFØ�A�=@Ø'=@ÝJ?Èß�Ø�AJÙ>�JàÈ?�; Ù6LJ?�ßICFÙ@CGØ�A#ÜJ;@Ø<HJEF?Ià-Ù>=@�JLJCF?IL�CGA �}?�ßI=@CFØ�A Mã�� ?1èO;>Ù>=�=K;>?�:\=�=@ÝJ?gß�:<Ù>?g×�ÝM?�;@?�� �� 3$CFA1��� �"%7ã���ÝM? â Ø<EFEFØ_×�CGAJ� ÜJ;@Ø<Ü Ø�Ù>CG=@CFØ�A+Ù>ÝJØ_×�ÙD=@ÝO:\=�CFA=KÝJCGÙ�ß�:<Ù>?6=@ÝJ?1á\:<EF�J? â �MAJßI=@CFØ�AJÙ ;8($LJ?7èOAJ?�L�HeÖ �tê �4%qÜ Ø�Ù>Ù@?IÙ@Ù0: ÜO:\;>=KCGß��JEF:<;@EhÖÈß�Ø�Aeá�?IAJCF?IAe= â Ø�;>à�ã���$% ��% �"$ �%&� �� D$<b.p5�5?7�9�;[<�*�2$4C5������ W6D 5BAC<�*K5 �&D8Q`A�4TQc5?7?;6;[2$5\D � �� 3 *+4()����$, _ sD��64TD�<=]TDRd3AI 7 DF5 ���(��$ � ê��������5�!� A�5k*+4 )��?, _ n!]&DB4j<=]TDpOZ2$I+I�2���*K4CE ]T2$I�Q 5�<=@?7�D _

)+*-,� l2$@ $ �&����������� A4TQ f (�)*� ���( <=]TD�dVA�IZ7 D OX7:4T0�<=*�2�465 ;H( QCD��64TD3QxWVG ) ���$, 5BA <=*K5SO+G

;8( � f ( �B� ( = % � (( & � . f ( - ���( 1�� ( �=� ( = %�� � �

��]TDF@VD ��� v ê A�4TQ�<=]&Db9fA8;6;T*K4CE 5 � ( Ú � ( �TY F GHG A�@VDUQCD��64TD3Q�@\D80$7�@�5�*Zd$DFImG�A�5��� �� � ( �=� ( = % � � ê -�� �( �Z� ( = % ������ � ��� ��� �( �=� ( = % � ��à3:D&! `b !#" � �%$ = < ( 3 5 & � . �1,( �tê ��& D 68("% -'&�� � 1�� ( G = �Z� ( = �B�(%�� � � � ( G = �=�

(= �!I �D% C �

)K*+*-, n!]TDb5V2$IZ76<=*#2$4�OX7:4T0�<=*#2$465bQ6D �64TD8Q *K4�D �C7 A <=*�2�4 ) � �3,s<ZA�� D <=]TDpOZ2$@S9

N � ( � f (`�\� ( = % � �N!( �=� ( = % � f ( - �� ("%] � ( � f (`�\� ( = % � �Yê � �N ( �Z� ( = %)%�� f ( - ���("%(&�( �Z� ( = %[ �( � f (`�\� ( = % � �Yê � �N ( �Z� ( = %)%�� f ( - ���("%��tê �N6 D( &�(8�=� ( = %B%�� �� (

OZ2$@bD\A�0^] $ � ê��������5�!� ��]TDB@\D �N!( �Z� ( = %�ÚT� � ê -)� �( �=� ( = % ���� � � Y = A�4&Q&�( �Z� ( = % ÚT� :<;>�yàË:(&! `b !#" � � $ = < ( 3 5 & � . �1,(8�Yê �*& D 68("% -'&�� � 1+�y( G = �Z� ( = �\�D% � � � � ( G = �=�(= �!I �D% Ce�

,.- 4VQ 0 4&E�0[>�!DQ Y�._Q !��VY-!/*�0 %'!2Q[Y�7K0IQ6>-#FzV! .�!/!2*�,1!/%'({z8!2, (:*�# Q 7:(:`8>�0[7:W ,�(�/ !/%'!/*�0 Q[!Z0 0'(+*-` .XW10�#89 #&*-Q'Q 4V* � j2gVl8g � \2 7+7�T�%[4X48E QP4&E�0[>�!=EU4V7+7:4B} (+*-`a%'!2Q[Y�7+0'Q #&%'!=T�7 #8HZ!�,M(:* 2 T�T�!/*_,1(�3 2 \ê !

Page 18: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

9DØ<=@CFAJ� â ;>Ø�à � $%R=KÝJ:\=7�� b�� �' = - �� = <Ð= â Ø�EGEFØ_×�Ù â ;>Ø�à ��;@Ø<Ü Ø�Ù>CG=@CFØ�A � :<AJL'? +}�J:\=KCGØ�A1�tê_ì$%R=@ÝO:\=:<A3Ø<ÜM=KCGà3:<EVLJ?�ßICFÙ>CFØ�A â Ø�;���� 36à3:�Ö H¹?ÆØ�HM=T:\CFAJ?IL â ;>Ø�à =KÝM? â Ø�EGEFØ_×�CFAM�1Ø�ÜM=KCGàËCG��:\=@CFØ�A ÜM;@Ø�HJEG?�à�Ú

àË:(&; � �E? � � -�� <%& �=N � � %_- ( 3 5 & � . 1�[j-*�� b -�] � � 1+� = �=�D% � ��� � = �@I �D% BBB [7� f � N �X] D 6 )*���� b ��1 C �

��� $%� AJ?1:<EGÙ@ØÉØ�HMÙ@?�;tá�?IÙ â ;>Ø�à =KÝJ?ICF;q;>?�ßI�J;@Ù>CGá�?gLJ?7èOAJCh=KCFØ<A+CFA ��;>Ø�Ü Ø<Ù@CG=@CFØ�A �6=KÝJ:\=�=KÝM? â �JAJß7=KCFØ<AJÙ � (MÞ$ �)ê��������&�!� :<;>?Ë?.&Vß�EF�MÙ@CGá<?�EhÖ�LM?I=K?I;@àÈCFAJ?IL HeÖ =KÝJ?Èß�Ø�AMÙ@�JàÈ?�; {ÙÉ?.&VÜ ?IßI=T:Ê=KCFØ<AJÙ �1 â Ø<; â �M=@�J;@?H Ø<AJL�;>?I=@�J;@AJÙ|:<AJL'=KÝJ?6LJCGÙ>=K;>CFHJ�V=KCFØ<A � â Ø�;Æ:<Ù>Ù@?I=DÜJ;>CFß�?IÙ|:\AJL�LMCGá}CFLJ?IAJLJÙIã�é1CGá�?IA�=@ÝJ?�Ù>?�;>?�Ù@�MEG=KÙ=KÝJ? â Ø�EFEGØd×�CGAJ��=KÝJ?IØ�;@?Ià ßTÝJ:<;K:<ß7=K?I;@CF�I?�Ù3=@ÝJ?�LJ?Ià3:\AJL â �JAJß7=KCGØ�AJÙ3LM?�;@Chá�?IL â ;@Ø�à � � $%7ã égChá�?IA=KÝJ?�ÜJ;@?7áVCGØ��JÙËLJ?�;>CGá\:\=KCGØ�AJÙÈ=KÝJ?�ÜJ;@Ø}Ø â CFÙÈÙ>=@;K:<CG��Ýe= â Ø�;t×�:\;@LÍHeÖ :<ÜJÜJEhÖVCGAJ�«åa?IàËàË:0! �<CGá�?IAÍCFA- ÜJܹ?�AMLJC & - ã��� ��%��$��� �

� *Zd$DF4/<�]TD�;lI A�4646*+4CEU]T2$@S*��$2$4 � )&ê I#D$<l.p5�587:9�;�<=*�2�465�� � �sW6DM5FAC<=*+5 �TD3Q A4TQs5?7?;6;[2$5\D � �� 36_� D$<pD �:;[D80�< AC<�*�2$465 �' %~F �G � �1 %2F ��Y =GHG A4TQ � % �,;>Ø�H�� �?� % WCD�E * d�DB4 _ 7:@?<�]TDB@S9R2�@VD � Q6D��64&D�� bc) 3 A�5b*K4 ) �?, A�4&QaI�D$<p<=]TD OX7�4T0$<�*�2$465 �y( � $ � ê����������!� W6D QCD��64TD3Q�A�5H*K4 �P@\2V;[2$5�*Z<=*�2�4 � _n!]TDB4/OZ2$@ A�I+I �@1a�@6 % � 3 A�4TQ f �9���� b���1 <=]TD�Q6DF9 A4TQ OX7�4T0$<�*�2$465e*+4 )�� � ,s<ZA�� D�<�]TDpOZ2$@�9

� � �@1a�@6 � f ���'�� �1c� � % � �N4�K1a�A6 � �1c� � %�� f - �� b���1F%��� �@1a�@6 � f ���'Z� �1a� � % � �tê � �N��@1a�A6 � �1a� � %)% � f -*�� b���1F% & �@1a�A6 � �1c� � %��� �@1a�A6 � f � ��� �\�'�� �1F% � �tê � �N��@1a�A6 � �1a� � %)% � f -*�� b���1F% �tê �N6 D& �@1a�A6 � �1a� � %B%�� �� b���1��� �A%

��]TDB@\D �N��@1a�@6 � �1c� � %�ÚT� � ê -)� � �K1a�A6 � �1a� � % ������ � Y = A�4TQ& �K1a�A6 � �1a� � % ÚC� :\;@�aàË:(&! `b ! " � $ = < ( 3 5 & � . 1 �tê ��& D 6 % -'&�� � 1+� = �=�(%�� � � � = �@I �D% C� � �K1a�A6 � �1a� � % ÚC� ��àË:(&! `b ! " � $ = < ( 3 5 & � . 1 �tê ��& D 6 % -'&�� � 1+� = �=�D% � ��� � = �@I �D% C��

� AJ?�Ø�HMÙ@?�;tá�?IÙ0=KÝO:\=Dß�Ø<AJÙ@�JàÈÜM=@CFØ�A�:\=D=@CFàÈ?�� � 3ÈCFÙÆ��CGá<?�A�HeÖ�: â ;@:<ßI=@CFØ�A �N4�K1a�A6 � �1a� � %�Ø â =KÝJ?Ù@�Jà Ø â ßI�J;@;>?�Ae=Æ×q?�:<EG=@Ý f :\AJL�=@ÝJ?1LJCGÙ@ß�Ø<�JAe=K?�L�?'&Vܹ?�ßI=@?�L�AJØ�AVÛÐß�:<ÜJCh=T:<E CFAJßIØ�àÈ?1Ù>=K;>?�:<à �� b���1Éã��ÝJCFÙ Ù>�Jà ×�CGEFE�H ?3ß�:<EGEF?�L �Lw n�p&o@w��0p0w����!x�0p ã �V�JßTÝ :�ß�Ø�AMÙ@�JàÈÜM=KCGØ�A«H¹?�ÝO:�á}CFØ<;ÉÙ>=@;@Ø�AJ�<EGÖ�Ù@�JÜVÛÜ Ø<;>=KÙ�=@ÝJ?·Ù>Ø\Û�ß�:<EFEG?�L'ܹ?�;@àË:<AJ?IAe=DCGAJß�Ø<àË?1ÝeÖ}Ü Ø\=KÝJ?IÙ@CFÙ �vÙ>?�?\Þ ?\ã{�JãhÞ � Ø�àË?I;1ê_ì�ì"!"%7ãqæqEF?�:\;@EGÖ<ÞJØ�AJEhÖ=KÝJ?�+r�O:<Ae=KCh=�Ö f CFÙÆLJCG;@?�ß7=KEhÖ�:_á\:<CGEÑ:<HMEF?0=KØË=KÝJ?·ß�Ø�AJÙ>�JàÈ?�;D×�ÝMCFEF?g=KÝM? +r�O:<Ae=KCh=�Ö��� b���1 ÝO:\ÙD=KØËH ?H Ø<;@;@Ø_×R?�L�HrÖ#CGÙ@Ù>�JCFAJ��H¹Ø�AJLJÙIã?��ÝJCGÙ·CGÙ0=KÝJ?È;@?�:<Ù@Ø�A â Ø�;1=KÝJ?È:<ÜMÜ ?�:<;K:<AMß�?ÈØ â =@ÝJ?È=@?�;>à ��� b �Z1CFA�=@ÝJ?ÉH¹Ø�AJL#LJ?�àË:<AJL â �MAJßI=@CFØ�A§ãF��ÝJ? Ø<ÜM=KCGà3:<EcCFAeá<?�Ù>=@àË?IAe=gCFA�Ù>ÝO:<;@?IÙgCFÙ0LJ?7=K?I;@àÈCFAJ?IL�HrÖ�=KÝJ?Ù@Ø�EG�M=KCGØ�A & �K1a�A6 � �1a� � %R×�ÝJCFßTÝ�CFÙq?'&Vß�EG�JÙ@Chá�?�EhÖ"LJ?7=K?�;>àËCGAJ?�L�HeÖ"ß��M;@;@?IAe=|:\AJL�?.&VÜ ?IßI=K?IL�èOAJ:<AJß�CF:<EÜJ;@CGß�?IÙ�ã

æqØ�AJÙ>CFLJ?I;0AJØ_×�=KÝJ?Éß�:<Ù@?·×�CG=KÝ�EFØ��e:\;@CG=@ÝJàÈCFß1�M=@CFEFCh=�Ö+×�ÝJ?I;@? �O� 33CFA ��� �"%ã �VCGAJß�?ÉCGA�=@ÝJCFÙDß�:<Ù>?=KÝJ? â �MAJßI=@CFØ�A�&�CFÙ�AJØ\=�LJ?IèJAJ?�L�:\=��I?�;@Ø - Ù@Ù@�MàËÜM=@CFØ�A ��àÉ�MÙ>=�H¹?0;@?IEÑ:(&V?�L"=@ØÈÝMØ�EFL+Ø<AJEGÖËØ�A"=KÝJ?

ê 2

Page 19: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

CFAe=K?I;@CGØ�;DØ â =KÝJ?�ß�Ø�AJÙ>�JàÈÜM=KCGØ�A�Ù>?I= � ã BÆØd×R?Iá<?�;IÞÏåÏ?IàËàË:�ê�CFàÈÜJEFCG?�Ù�=KÝO:Ê=D=@ÝJ?�×R?�:<Eh=KÝ�ÜJ;>ØVßI?�Ù>Ù� ��( � g �\� ( = %)%

�(� = CFAJLJ�Mß�?�L HeÖ :<AeÖ Ü Ø<=@?�Ae=KCF:<EFEhÖ Ø<ÜM=KCGà3:<EqÙ>=K;@:\=K?I�<Ö � L � g % %B�@1a�A6 � f %�ÝO:<Ù

=KØ'ÙK:Ê=KCFÙ â Ö ��( � g �\� ( = %J� � ���( � � :Mã Ù�ã � =KÝJ?I;>×�CGÙ@?$Ø�AJ?$?�:\Ù@CFEhÖ�Ù>ÝJØ_×�Ù6=@ÝO:\= N!( �=� ( = %�� 3+×�CG=KÝÜ Ø<Ù@CG=@CGá<?�ÜJ;@Ø<HO:<HJCGEFCG=�Ög×�ÝJCGßTÝ$CFàÈÜJEFCG?�Ù ,?- .0* b(� L � i %21 � �

d ; b �@1a�A6 � f %7ã <Ð= â Ø�EGEFØ_×�Ù â ;>Ø�à =@ÝJCFÙØ�HJÙ>?�;>á\:\=@CFØ�A"=@ÝO:\=�=KÝJ?gLJ?Iß�CGÙ@CFØ<A�ÜM;@Ø�HJEG?�à ��ì$%q;>?�àË:<CFAJÙ�×R?�EGEhÛÐLJ?IèOAM?�L�?Iá�?IA�CGA'=@ÝJ?gEFØ�� ß�:<Ù@?\ã��Ø :<EGEF?Iá}CF:\=K?�=@ÝJ? Ù@�JHJÙ>?�+r�J?IAr=�AJØ<=T:Ê=KCFØ<A ×R? LJ?IèOAM? ( (&ÚC� êc- ( - ����� - (

��Y\( â Ø�;"?�:<ßTÝ$ � 3���ê��������&�!��ã���ÝJ? â Ø�EGEFØ_×�CFAJ��;@?�Ù>�JEG=�?IÙ>=K:<HJEFCGÙ@ÝJ?IÙ�=KÝJ? â Ø�;>à Ø â =KÝJ?1á\:<EG�J? â �JAJß7=KCFØ<AJÙ â Ø�;�=KÝJ?EFØ��ÊÛ��M=@CFEFCh=�Ö$ß�:<Ù>?<ã���$% ��% �"$ �%&� �� D$<[.b5S5?7:9s;[<�*�2$465 � � �JWCD 5BA <=*K5 �TD8Q�A�4TQJI#D$< � � 3 *K4 )����$, _ n!]TDF4`<�]TD OZ2$I+I�2���*K4CE�]T2$I#Q�5�<=@87 D��

)+*-,� l2$@ $ �&ê������������ A4TQ f (�� � �� ( <�]TD�d3AI 7 D OX7:4&0$<=*#2$465 ;8( Q6D��C4TD8Q W3G ) ���$, 5FAC<=*+5�O+G;8( � f ( �\� ( = %�� ( (�EFA � f ( - �� ( � -��y( �Z� ( = %��]TDF@VD <=]TDpOX7:4T0�<=*#2$465 � ($Ú � ( �lY F A�@\DUQ6D��64&D8Q�@\D80�7:@�5S* d$DFImG�A�5 �Z� v 3 A�4TQ

� ( �=� ( = % � àË:(&! `b � " � $ = � � ( (�� êD%)3 5 EFA � �1 ( �Yê ��& D 68("% -'&�� � � � ( G = �=�(= �!I �D% BBB & D 6�( ê �

- ( 3 5 �y( G = �Z�(= �\�D% � ( G = �=�

(= �!I �D%_- � ( (�� êD%MEGA � ( (��ÍêD%�� ( (�EGA � ( ($% �

)K*+*-, n!]TDb5V2$IZ76<=*#2$4�OX7:4T0�<=*#2$465bQ6D �64TD8Q *K4�D �C7 A <=*�2�4 ) � �3,s<ZA�� D <=]TDpOZ2$@S9

N � ( � f ( �\� ( = % � �N!( � f ( - �� ("%] � ( � f ( �\� ( = % � �Yê � �N (4%�� f ( - ���("%(&�(8�=� ( = %[ �( � f ( �\� ( = % � �Yê � �N (4%�� f ( - ���("%��tê ��6 D( &�( �=� ( = %)%�� ���(

OZ2$@bD\A�0^] $ � ê��������5�!� ��]TDB@\D �N!($ÚT� �÷êe- ( ( �Y =eA�4TQ

&�(8�=� ( = % ÚT� :<;@�¹àË:(&! `b !#" ��� $ = < 3 5§EGA � �1,( �tê���& D 68("% -'&�� ��� � ( G = �Z�(= �!I �D% C �

5Æ=@CFEFCG��CGAJ� ��;>Ø�Ü Ø<Ù@CG=@CFØ�A :<AJL"=KÝJ? â :\ßI=�=@ÝO:\=�?�+r�O:Ê=KCFØ<A �� $%RCGàËÜMEFCF?IÙv�� b�� �' = - �� = ÞJØ�AM?1Ø�HM=T:\CFAJÙâ ;@Ø�à �Yê_ì$%�=@ÝJ? â Ø�EGEFØ_×�CFAM�ÈØ<AJ?7ÛÐÙ>=T:\��?ÉLJ?Iß�CFÙ>CFØ�A�ÜJ;@Ø�HMEF?�à â Ø�; ��� 33LJ?IèJAJ?�L â Ø�;D:<EFE �@1a�@6 % � 3:<AJL f � ���� b ��1ÉÚàË:(&

;�� �E?� � -�� < EGA ��N�% - � ( b �ÍêD% 3)5ÊEGA � � �@W �\������ b��!1F% � � = �KI �D% BBB N -h[j-�] D 63� f ��[ )*��� b �Z1 C � ���"#"%BD?I;@? ( b6ÚC� �Yê�- ( - ������- (

� %D:<AML�=KÝJ? :\LJLJCG=@CGá<?�ß�Ø<AJÙ>=K:<Ae=��Zb·ÚC� � 5 � = �=�(% � = �KI �(%ÆÝO:<Ù0H¹?�?IAØ�àÈCG=@=@?�LçÙ>CFAJßI?"CG= LJØ}?�Ù AMØ<=È:�� ?�ßI= =@ÝJ?'Ù@Ø�EG�M=KCGØ�A =@Ø�=KÝJ?'ÜJ;>Ø�HJEF?Ià�ã15Æ=@CFEGCF��CGAJ��åa?IàËàË: !�=KÝJ?Ø�ÜM=@CFàË:<E%ßIØ�AJÙ@�MàËÜM=@CFØ�A :<AML�CGArá<?�Ùt=KàÈ?�Ae=�LM?�ß�CGÙ@CGØ�A â Ø<;���� 3'ß�:<A H ?ÈLJ?I=@?�;>àËCGAJ?�L â ;@Ø<à � �"#4%7ã��ÝJ? ;@?IÙ@�JEh=KCGAJ� â Ø�;@à/Ø â =KÝM? LJ?�àË:<AJL â �JAMßI=KCGØ�AJÙ1CGÙ|Ù>=K:\=K?IL�CGA�=KÝM? â Ø�EFEGØd×�CGAJ�Ë=@ÝJ?�Ø<;@?�à�ã·égChá�?IA=KÝJ?6ÜJ;>?Iá}CFØ��MÙÆLM?�;@Chá\:\=KCGØ�AJÙ�=KÝM?6ÜM;@Ø}Ø â CGÙ�:<�e:<CGA�Ùt=K;@:<CF��Ýe= â Ø�;>×q:<;@L'HeÖ�:<ÜJÜMEGÖ}CFAJ�Èåa?�àÈàË:�! ��Chá�?IACFA - ÜMÜ ?IAJLJC & - ã

ê >

Page 20: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

��� ��%��$��� �� D$<�.b5�587:9s;[<=*#2$465 � � � WCDf5BAC<�*K5 �&D8Q A4TQ 587?;6;[2$5VD � � 3 *+4 ) � �$, _ � D$<�<=]&D/032$465?7�9RDF@#� 5;lI�A4646*K4 E�]T2$@S*��$2$4 � )-ê A�4&Q D �:;�D30$<ZAC<=*#2$465 �' %gF �G � �1 %gF ��Y =GHG A4TQ�� % ��;@Ø�H � � � % W6DE * d�DB4 _ 7:@8<=]TDF@�9�2$@VD � Q6D��C4TD �� b�) 3 A�5 *+4 )��?,RA�4TQ <�]TDR9fA�@SE *+4 A�IbQ�*+5?<�@�*�W 76<=*#2$4 � = A�5 *K4� DB9q9 A � _ n!]TDF4jOZ2�@�A�IKI �@1a�@6 % � 3 A�4TQ f �}��� b��Z1 Q6D�<XDF@�9q*K4TD3Q`W3G ) �V,�<=]TD 032$465?7�9RDF@#� 5Q6DB9fA�4TQcWCDB] A d�*�2$@b0\A�4`W6D�Q6DF5V0B@S*�WCD8QcWVGj<=]TDpOX7:4&0$<=*#2$465

� � �@1a�A6 � f � � = �l�'�� �1 % � �N4� f - �� b��Z1F%� � �@1a�A6_� f � � = �\�'�� �1F% � �tê � �N %�� f -9�� b ��1F% & �@1a�A6 � � = %��� �@1a�@6 � f � � = �l�'�� �1F% � �tê � �N %�� f -9�� b ��1F% �tê ��6 D& �@1a�A6 � � = %B%�� �� b ��1���4!$%

��]TDB@\D �N0ÚT� � ê - ( -U����� - (� � Y = A�4TQ

& �K1a�A6 � � = %�ÚC� :<;@�aàË:(&! `b !#" � $ = < 3 5 � EFA � 1 �tê ��& D 6 % -'&�� � � � = �@I �D% C � ���"2"%

æqØ�àÈÜO:<;@?ILÈ=@Ø1=KÝJ?ÆÜJ;@?7á}CFØ��JÙ,ß�:<Ù@?�×�ÝJ?�;>? � �� 31=KÝJ?�Ar�JàÉH¹?�; �N�LJ?7èOAJCFAM�6=@ÝJ?�à3:<;>��CFAJ:<EMÜJ;>Ø�ܹ?�AVÛÙ@Ch=�Ö"=KØÈß�Ø�AJÙ>�JàÈÜM=KCGØ�A ��Ø��M=ÆØ â EFC â ?7=KCGàË?0CGAJß�Ø<àË? %qLJ?�ܹ?�AJLMÙ|?'&VßIEF�JÙ>CGá�?IEGÖ'Ø�A�=KÝJ?6Ù@�MH��>?�ß7=KCGá<?�LJCGÙtÛß�Ø��MAr= â :<ß7=KØ�; ( :<AML'=@ÝJ?1ß�Ø<AJÙ@�JàÈ?�; {Ù�;>?�àË:<CFAJCGAJ�ÉEGC â ?I=@CFàÈ? ��ã ��ÝJCFÙ�CGàËÜMEFCF?IÙ�=@ÝO:\=�=@ÝJ?1Ø�ÜM=@CFàË:<Eß�Ø�AMÙ@�JàÈÜM=KCGØ�AÈLJ?�ßICFÙ@CGØ�A$CFÙ,CFAMLJ?�ܹ?�AJLM?�Ae=qØ â :<AeÖ$?.&Mܹ?�ß7=T:\=@CFØ�AMÙ â Ø�; â �V=K�J;>?|:<Ù>Ù@?7=qÜJ;>CFßI?�Ù�:<AJLÈLJCGáeÛCFLJ?IAJLJÙIã���ÝM?·;>?�àË:<CFAJCGAJ�ÉEGC â ?I=@CFàÈ?DCGAJß�Ø<àË?��Yê � �N�% � f -*�� b���1F%�CFÙ�CGArá<?�Ùt=K?�L�CFAe=KØ =@ÝJ?gÙK: â ?g:<Ù>Ù@?7=/ � 3�:<AJL+Ù>ÝO:<;@?IÙ�/ ��ê��������5� + ã�<�A3=@ÝJCFÙR;@?I�e:<;@LyÞV=KÝM?1:<àÈØ��JAe=qCGAeá�?�Ùt=K?IL�CGA+Ù@ÝJ:<;@?IÙ�CFÙRLJ?I=@?�;tÛàËCGAJ?�L�HrÖ�=KÝM?ÉÙ@Ø�EG�M=KCGØ�A &$=KØ ���"2"%ã@��ÝJ? Ùt=K;@�MßI=K�M;@?ÉØ â =@ÝJCFÙDÜJ;@Ø<HJEF?Ià/ßIØ�;@;>?�Ù>Ü Ø�AMLJÙ1?'&M:<ß7=KEGÖ�=KØ=KÝJ?ÆܹØ�;>= â Ø�EFCGØ1LJ?�ßICFÙ@CGØ�AÈÜJ;@Ø�HMEF?�à�Ù>Ø�EGá<?�LËHrÖÈ:6ß�Ø�AMÙ@�JàÈ?�;,×�CG=@Ý3:6Ø�AJ?7ÛÐÜ ?I;@CGØVL$ÜJEF:<AJAJCGAJ�gÝJØ�;@CG��Ø�A×�ÝJØ+CGÙD?IAJLJØ_×q?IL�×�CG=KÝ�Ø�AJ?·�JAJCG=DØ â ×R?�:\EG=KÝ�:<AJL�×�ÝJØ3CFÙÆAJ?�Ch=KÝJ?I;0:<EGEFØ_×q?IL�=@ØË=T:��<?�Ù>ÝJØ�;t=0ÙK:\EF?�ÙAJØ�;�ßI;@?�LMCG=�ã <�A$ÜO:<;>=@CFßI�JEÑ:<;IÞ<AJØg?.&Mܹ?�ß7=T:\=@CFØ�AMÙ â Ø�;�:<Ù>Ù@?I=,ÜM;@CFßI?�Ù,:<AMLÈLMCGá}CFLJ?IAJLJÙk×�ÝJCGßTÝ$EFCF? â �J;>=@ÝJ?�;=KÝO:\A�Ø�AJ? ܹ?�;@CGØVL�:<ÝJ?�:\L�?�Ae=K?I;0=KÝJ? ÜJ;>Ø�HJEG?�à�ã ��ÝJCFÙ0ÜM;@Ø�ܹ?�;t=�Ö�CFÙ|ß�:<EGEF?�L�ß�Ø�àÈÜJEF?7=K?·à�Ö�Ø�ÜMCÑ:+Ø�;à�Ö�Ø<ÜJCFß�CFAeá<?�Ù>=@àË?IAe=qH¹?�ÝO:�á}CFØ<;R:\AJLËCGÙ�×q?IEFEhÛ �rAJØ_×�AÈ=@Ø·ÝJØ<EFL ×�CG=@ÝËEGØ��e:<;>CG=KÝMàËCGßR�M=@CFEGCG=�Ö�Þ<Ù@?�?\ÞV?\ã{�MãGÞ<�AJ��?I;@Ù@Ø<EFE=�Yê_ì">$24%7ÞyØ<;1B|:4�Ê:<AMÙ@Ù@Ø<A �Yê_ì$243"%7ãF9DØ\=K?�=@ÝJØ��J��Ý�=@ÝO:\=1?.&Mܹ?�ß7=T:\=@CFØ�AMÙ â Ø�; â �M=@�J;@?�H Ø�AML;@?7=K�J;>AJÙ|:\AJL'AJØ�AVÛÐß�:<ÜJCh=T:<EyCFAJßIØ�àË?|Ù>=K;>Ø�AJ��EhÖ"CFA��O�J?�AMß�?1=KÝJ?gLJ?Iß�CGÙ@CFØ<A'=@ÝJ;@Ø<�J��Ý'=KÝJ?1=K?I;@à �� b�ã� ?ÈAJØ<=@? â ;>Ø�à)=@ÝJ?ËCGAe=K?��<;K:<E�CGA ���"2"%|=KÝJ:\=6Ø�AJEGÖ�=KÝJ?ÈÙ@�Jà Ø â AJ?.&V=�Ü ?I;@CGØVL ÙgÜJ;@CGß�?IÙ�:<AML�LJChá}ChÛLJ?�AMLJÙ � = � �:6 = ��I = %1?IAe=K?�;g=KÝM?ÈÜM;@Ø�HJEG?�à LJ?IèOAMCFAJ�'=KÝJ?$ßI�Jà$ÛÐLJCGá}CGLJ?�AJL#ÜJ;>CFßI? � ÚT� 6 = -|I = Ø â=KÝJ? â Ø�EFEGØd×�CGAJ�$Ü ?I;@CGØVL§ã ��ÝJCGÙ|Ù>�Jà H¹?�CGAJ�":ÈàË?�:<Ù@�J;@:<HJEG? â �JAJß7=KCGØ�A�Ø â =KÝJ?É;@:<AJLJØ<à á\:<;>CÑ:<HMEF?s� =Ü ?I;@àÈCG=@Ù��JÙ�=KØ$LJ?IèJAJ?6:<A�CGAJLJ�JßI?�L�àË?�:<Ù@�M;@? �� â Ø�;�=@ÝJ?g;K:<AMLJØ�à á\:<;>CÑ:<HMEF? � ßIØ�;@;>?�Ù>Ü Ø�AMLJCFAJ�$=KØ=KÝJ?ÈCFàË:<��?�àË?�:<Ù@�J;>?ËCGAJLJ�JßI?�L HeÖ � = ã3æqEF?�:\;@EGÖ<ÞÏÙ@CFAMß�?ÈHrÖ ��CFC %DØ â - Ù@Ù>�JàËÜV=KCFØ<A #":<AJL åa?�àÈà3:ìMÞ � = CFÙ$Ù>�JÜJܹØ�;>=@?�LÍØ�A =KÝM?�ßIØ�àËÜJ:<ßI=ËÙ@?7= �� = � � Þ�=@ÝJ?�Ù>�JÜJܹØ�;>=ËØ â �� ×�CFEFEqH ?�:�ßIØ�àËÜJ:<ßI=Ù@�JHMÙ@?I= �� � F BGHG ã#ä &VÜJEGØ�CG=@CFAJ��=KÝJ?+ßTÝJ:<AJ��?Û�Ø â Û±á<:\;@CÑ:\HJEF? â Ø�;@à��JEÑ:'=KÝJ? â �MAJßI=@CFØ�AçCGA:� �"24%6ß�:\A?�+r�JChá<:\EF?�Ae=@EGÖ+H¹?gLJ?IèJAJ?�L�:<Ù

�& �@1a�A6 � �� %qÚT� :<;>�,à3:(&! � � <!3�EGA �K1�-)& D � � �21e6 %)% ��� �@I � % BB & D 6 ê C �

� ?Ëß�EGØ�Ù@?È=KÝJCGÙ·Ù>?�ßI=@CFØ�A ×�CG=@Ý�=KÝM? â Ø�EGEFØ_×�CFAJ�'ßIØ�;@Ø�EGEÑ:<;tÖ�×�ÝJCGßTÝ«Ù@ܹ?�ßICÑ:<EGCF��?IÙ���ÝM?�Ø�;>?�à ��=KØ�=KÝJ?ß�:<Ù>?6×�Ch=KÝ�: Ù@CGAJ��EF?1;>CFÙB�rÖ":<Ù@Ù>?I=�×�ÝJ?�;>?a+ � ê�ã���ÝM?·ÜJ;>ØVØ âcâ Ø<EFEFØ_×�Ù�CGàËàÈ?�LJCF:\=K?IEGÖ<ã

ê�ì

Page 21: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

� %��$%���������� �� 4TQCDB@ <�]TDU]:G ;�2�<=]TDF5VDB5�2�Opn!]TD82�@VDB9 ��587?;6;[2$5VD + � ê _ n!]TDB4 <�]TD Q6DF9 A�4&Q�OX7:4T0�<=*#2$465f) � �3,< A���D <�]TDpOZ2$@�9

� � �K1a�A6 � f � �� �`�'�� �1F% � �N�� f - �� b���1F%��� �K1a�A6 � f � �� �l�'�� �1F% � �Yê�� �N�% � f -*�� b ��1F%��& �@1e6 � ��� % �&6��� �@1a�A6 � f � ��� �l�'�� �1F% � �Yê�� �N�% � f -*�� b ��1F% �tê � �& �K1e6 � �� %)%�� �� b���1��]TDB@\D �N *+5aQ6D �64TD3Q A5RA6WC2 d�D/A�4TQ <�]TDR5S] A�@VD>2$O�)KI+*KOZD$<�*K9�D�,q*+4T082$9�Df*K4&d$DF5?<XD3Q *+4 5S] A�@VDF5�*K5Q6D$<�DB@S9J*+4TD8QcWVGj<=]TD�032$4&<=*K4&7 2�7:5k9 A8; �& � i � �� %qÚ F GHG �lY . 3���ê 1

�& � � � ��� %qÚT� :<;@�$àË:(&�! ��� b =�� < 3 � EFA � � - �& � � � � %)% �� �@I � %/C �

� � �����/������������

��ÝJCFÙ·ÜO:<ܹ?�;·Ø4�y?I;@Ù�:���?�AM?�;K:\ERàË:\=KÝM?�àË:\=KCGß�:<E â Ø�;>àÉ�JEF:\=KCGØ�A�Ø â :�à��JEG=@ChÛ�ܹ?�;>CFØ}L�ß�Ø�AMÙ@�JàÈÜM=KCGØ�AVÛCFAeá�?IÙ>=@àË?IAr=�ÜJ;>Ø�HJEG?�à CGAÉ=KÝJ?�ÜM;@?�Ù>?�AJßI?DØ â �JAMß�?�;t=T:<CGAe=�Ö LJ�J?�=@Ø6Ùt=KØ}ßTÝO:<Ùt=KCFß�CGAeá�?�Ùt=KàÈ?�Ae=�Ü Ø<Ù@Ù@CGHJCFEoÛCG=@CF?�ÙIã Cq:<Ù@?ILÉØ�A�=@ÝJ?qAJØ\=KCFØ<A�Ø â :Æß�Ø�AMÙ@�JàÈÜM=KCGØ�AVÛÐCFAeá�?IÙ>=KàÈ?�Ae=%Ù>=K;@:\=K?I�<Ö·:|àÉ�JEh=KCoÛ�ܹ?�;@CGØVL1?.&VÜ ?IßI=K?IL�M=KCGEFCh=�Ö à3:D&MCGàËCG��:\=@CFØ�A ÜM;@Ø�HJEG?�à�×q:<Ù â Ø�;>àÉ�JEÑ:Ê=K?�LÈ�JAJLM?�;���?IAJ?�;@:<E :<Ù@Ù>�JàËÜV=KCFØ<AJÙqØ�A3ÜJ;@? â ?�;@?IAJß�?IÙ:<AJL'?'&Vܹ?�ß7=T:\=@CFØ�AJÙIã���ÝJ?g?'&VCFÙt=K?IAJß�?g:<AML�ÜM;@Ø�ܹ?�;t=KCF?IÙ�Ø â :ÉÙ@Ø<EF�M=@CFØ�A3=@ØÉ=KÝJ?|ÜJ;@Ø�HMEF?�à ×R?�;@?gÙt=K�JLVÛCF?IL«�JAJLJ?I;É��?IAJ?�;@:<Eq:\Ù@Ù@�MàËÜM=@CFØ�AMÙÉ:<Ù6×q?IEFER:<Ù â Ø�;g=KÝJ?ËÙ@ܹ?�ßICÑ:<E�ß�:<Ù>?3×�CG=@Ý æ � � - ÜJ;@? â ?�;@?IAJß�?IÙÜ ?I;@àÈCG=>=KCFAM��ß�EFØ<Ù@?�L â Ø�;>à Ù@Ø�EG�M=KCGØ�AJÙIã ��ÝM? â Ø�;>àÉ�JEF:\=KCGØ�A«Ø â : LJ?Ià3:\AJL â �MAJßI=@CFØ�A ÜO:<;@:<àÈ?I=K?I;tÛCF�I?�L�CGA�ßI�J;@;>?�Ae=1ÜJ;>CFß�?IÙ�Þ�×q?�:<EG=@Ý�:<AML�?'&Vܹ?�ßI=K:\=KCGØ�AJÙDØ4�y?I;@Ù|:Ëß�Ø<Ará<?�AJCG?�Ae=1ܹØ�Ù@Ù>CFHJCGEFCh=�Ö3=KØË�M=KCGEFCG��?=KÝJ?$;>?�Ù@�MEG=KÙ1Ø â =@ÝJCFÙ1ÜJ:<Ü ?I;1CFA�àË:<ß�;>ØV?Iß�Ø�AMØ�àËCGßÉ:<AML#èJAO:<AJßICÑ:<EkàÈØ}LJ?�EGÙ|×�CG=@Ý��JAJß�?I;>=K:<CFAe=�Ö#:<AMLß�Ø�AMÙ@�JàÈ?�;>Ù â :<ßICFAJ�È:Ëà��JEG=@ChÛ�ܹ?�;>CFØ}L+ÜJEF:<AJAJCGAJ�$ÝJØ�;@CG��Ø�Ayã - èO;@Ùt=0:<ÜMÜJEFCGß�:\=@CFØ�A"àË:�Ö'H ? â Ø��JAML�CFABDCGEFEF?IHJ;K:\AJL� ��3"3$2"%k:<AML CØ�ÝJà � BDCFEGEF?IHJ;K:<AML� �4343$2"%c×�ÝJØ6Ù>=@�JLMÖ =@ÝJ?�;@Ø�EG?�Ø â Ü ?IAJÙ@CGØ�A$Ù>Ö}Ù>=@?�àÈÙCFA�: Ù>=@ØVßTÝO:\Ù>=KCGß � åcé àÈØ}LJ?�Ey×�Ch=KÝ�àÉ�JEh=KChÛÐÜ ?I;@CGØVLËEFCGá<?�L'ß�Ø<AJÙ@�JàÈ?�;>Ù�ã ��ÝJ?6ÜJ;@Ø<Ü Ø�Ù>?�L�Ù>=@;@�Jß7=K�J;>?Ø â =KÝJ?�LJ?Iß�CFÙ>CFØ�A$ÜJ;>Ø�HJEG?�à Ù>ÝJØ��JEGL3:\EFÙ@Ø1Ø��y?I;,:6��?IAJ?�;@:<EFEhÖÉ:\ÜJÜJEFCGß�:<HMEF? â ;@:<àË?7×qØ<;)� â Ø<;�àËØ�Ùt=,LJ?�ßIChÛÙ@CGØ�A�ÜJ;>Ø�HJEG?�àÈÙÆCGA�ܹØ�;>= â Ø�EFCGØÉ=KÝJ?IØ�;>Ö�:<AML�Ù>=@ØVßTÝJ:<Ù>=@CFß6à3:<ßI;@Ø}?�ßIØ�AJØ�àÈCFßIÙ�ã�9�Ø}LJChèOß�:\=@CFØ�AMÙÆØ â =KÝJ?ÜJ;@Ø<Ü Ø�Ù>?�L#Ù@?7=K�JÜ�=@Ø"CFAJßIEF�JLM?�Ù@ÝMØ�;>=1Ù>?�EGEFCFAM�+:<AJL 7\Ø�;|=@ÝJ?ÉàË:(&VCFàÈCF��:Ê=KCFØ<A�Ø â ?'&VÜ ?IßI=@?�L �M=KCGEFCG=�Ö'Ø â=K?I;@àÈCFAO:<E¹×q?�:<EG=@Ý�:\;@?gÙ>=@;K:<CG��Ýe= â Ø�;t×�:<;>L§ã

��3

Page 22: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

� � ��� � �� ������� ����� ��� � �������� ��� �������������������

<Ð=1Ù@���ËßI?�Ùg=KØ"Ù>ÝJØ_× =@ÝO:\=0=@ÝJ?�;>? ?'&VCFÙt=KÙg:<A��JÜMÜ ?I;0H Ø<�JAJL �*�Ù>�JßTÝ�=KÝO:\=/,>- .0* b(� L � i %21 �* â Ø�;:<EFE � L � g % %

B�@1a�@6 � f %ã1åa?I= � L � g % %

B�K1a�A6 � f %ÆH¹?É:<;>HJCG=@;K:<;tÖ�ã <Ð=|Ù@���ËßI?�Ù1=KØ3Ù@ÝJØ_×&=KÝO:\=* b(� L �\� � = % d �* â Ø�;%:<EFEC� � = % �� ã��VCGAJß�? �� � �� = Va�������lV �� �'×�Ch=KÝÉ?�:<ßTÝ �� (RH¹?�CFAM�0ß�Ø�àÈÜO:<ß7=k=KÝM?�;@?

?'&VCFÙt=��JÜMÜ ?I;�:<AJL3EFØ_×q?I;RH¹Ø��JAMLJÙqÙ�( %c� :<AJL ���( %c� Ù@�JßTÝ+=@ÝO:\=�Ù

�( ��( ���( � Ûk:Mã Ù�ã â Ø�;,?�:<ßTÝ

$ � ê��������&�!� ã �}?I=@=@CFAJ�3?<ã �JãgÙ�ÚT� àÈCFA �dÙ

�( � $ � ê��������5�!�#"Ë:<AJL ��ËÚT� à3:D& �dÙ

�( � $ � �������5�!�#"

=KÝJ?IÙ@?gH¹Ø��JAJL"ß�:<A'H ?0ßTÝMØ�Ù@?IA�CGAJLJ?�ܹ?�AMLJ?�Ae=KEhÖ"Ø â $ ãq9�Ø�;@?IØdá<?�;IÞOEF?I=>=KCGAJ�E+�ÚT� Ü�-«L�Þ �� ÚC� �6j- �I

:<AJL � (�ÚC� 68(�-sI�( â Ø<;1?�:<ßTÝ $ � ê��������5�!� CG= â Ø�EFEGØd×�Ù0=@ÝO:\= 3�� Ü� 68( �6 � ÛD:Mã Ù�ã$:<AML

3�� +� �� ( �� � Ûa:Mã Ù�ã â Ø�;c?�:<ßTÝ $ � ê��������&�!��ã%ë0?IèOAM?R=KÝM?R×R?�:<Eh=KÝ�ÜM;@Ø}ß�?�Ù>Ùe����( � g �\� ( = % "

�(� =:<Ù@Ù>ØVßICÑ:\=@?�L ×�CG=KÝ Ù>=@;K:\=@?��<Ö � L � g % %B�K1a�A6 � f %0:<Ù·CGA ���"%7ã?CRÖ�á}CF;t=K�J?$Ø â ë0?IèOAJCh=KCGØ�A ��:<AML

åa?�àÈà3: ê�×q?�ÝJ:_á<? N&b f - �� b���1 :\AJL N ( �Z� ( = % ��( � g �\� ( = %e- ���( â Ø<;+?�:<ßTÝ � ( = % � ( Þ$ � ê��������5�!��ã <Ð=0CGÙÆ=@ÝJ?�;>? â Ø�;>?ÉÙ@���ÈßICF?�Ae=0=@Ø3ÜJ;>Ø_á�?�=@ÝO:\= â Ø<;D?�:<ßTÝ $ � ê��������&�!� =@ÝJ?�;>?É?'&VCGÙ>=KÙ���( % F Ù@�JßTÝ�=KÝO:Ê=

��( � g �\� ( = % ���( � ÛR:Mã Ù�ã ���4>$%� ?1ÜM;@Ø_á�? � ��>$% â Ø�; $ �&ê6:<AML'=@ÝJ?�A�:<ÜMÜJEGÖ+:<A'CFAJLJ�MßI=KCGØ�A":<;>���JàÈ?�Ae=�ã��cØ =KÝJCGÙ�?�AJLyÞOAJØ<=K?0=@ÝO:\=:<AeÖ CFAeá�?IÙ>=@àË?IAr=ËLJ?Iß�CFÙ>CFØ�A �K[Zb��^] b.%ÉàË:<LJ?�:\=$Ùt=T:<��? $ � 3#ÙK:\=@CFÙ>èJ?�Ù =KÝJ?�HJ�JLM��?I=Èß�Ø<AJÙ>=@;K:<CGAr=N&bz-Q[Zb,- ] Db 6 � f ã 5�=KCGEFCF�ICFAJ� åa?�àÈà3:Íê#Ø�AJ?#Ø�HV=T:<CGAJÙ"H Ø<�JAJLJÙ'Ø�A =KÝJCGÙ"CFAeá�?IÙ>=@àË?IAr=�:<Ù��� b���1 [Zb f �ÉÚ �[�bÉ:<AJLX] ; " ?b � f - �� b���1F% � 6 ; " ? �ÉÚ �] ; " ?b â Ø�;6?�:<ßTÝX/ �)ê��������5� + ã�V?I=>=KCGAJ� �] b|ÚT� � �]_;>=@?b ��������� �]_;LB�?b %MD���Chá�?�Ù

� = � g �\� = %�� �' = -h1#[Zb -2] Db � = �' = -k1 �[�b - �] Db �� = �ÉÚ �� = � ÛR:Mã Ù�ãCRÖ�×q:�Ö�Ø â CFAJLJ�MßI=KCGØ�A§Þ§Ù>�JÜJܹØ�Ù@? =@ÝO:\= â Ø�;1Ù>Ø�àË? $k% �rê��������&�!� � ê�"$=KÝJ?I;@?$?'&VCFÙt=KÙ6:<A#�JÜJܹ?�;H Ø<�JAJL ���(+Ù@�JßTÝ#=KÝO:Ê= ��( � g �B� ( = % ���( � ÛD:Mã Ù�ã�åÏ?IàËàË:�êÈ:<AJL�=@ÝJ?$CFAJLM�JßI=@CFØ�A�ÝeÖ}ܹØ<=KÝJ?IÙ@CGÙCFàÈÜJEGÖ�=KÝO:Ê=È=@ÝJ?�CFAeá�?IÙ>=KàÈ?�Ae=3ÜJEÑ:<AMÙ[y( � i % :<AMLk]H( � i % :\=ËÙ>=K:<��? $ ÙK:\=@CFÙ â Ös� ���( [y( �=� ( = % ��( � g �\� ( = % ���(*�ÉÚ �[Z( � Û3:Mã Ù�ã5:<AJLg]_; " ?( �Z� ( = % � ��( � g �\� ( = % - �� ($% �&6 ; " ?( � ���(0-�� ("% �ÊÜ

�; " ? �ÉÚ �]_; " ?( � ÛR:Mã{ÙIã â Ø�;�?�:<ßTÝ / ��ê��������5� + ã �V?7=@=KCGAJ� �]H($ÚC� � �]_;>=@?( ��������� �]_;CB�?( %MD#��CGá<?�Ù

��( G = � g �\� ( G == %�� �'�( G = - �1,(�[Z( �Z� ( = %l-3]H( �Z� ( = % D � ( G = �'�( G = - �1,( �[y( - �] D( �� �ÉÚ ���( G = � ÛR:Mã Ù�ã×�ÝJCFßTÝ�ÜJ;>Ødá<?�ÙÆ=KÝJ?gß�EF:<CFà � ��>$%7ã,ä�+r�O:\=@CFØ�A1� ��>$%�:<AJL�åa?�àÈà3:+êgCFàÈÜJEhÖË=@ÝO:\=

N!( �Z� ( = % �N!($ÚT� ���( - ���( � ÛR:Vã{ÙIãâ Ø�;�?�:\ßTÝ $ �&ê������������ :<AJL§ÞO?.&MÜMEFØ�Ch=KCFAM�É=KÝJ?gàÈØ�AJØ<=@Ø�AJCFßICG=�ÖÈØ â &

*�b(� L �B� � = %��:& ��N&b.% - �'(� =6(

( & �=N!( �Z� ( = %)% �*&ÚC��'(� 8b (

( & � �N!("% � ÛR:Mã Ù�ã��ÝJ?qEF:<Ù>=c? +}�J:\=KCGØ�A�CGàËÜJEGCF?IÙy=KÝO:Ê=?,?-/.0*�b(� L � i %A1 �* â Ø�;c:<EFE � L � g % %

B�@1a�@6 � f %a:<AML·=KÝM?�;@? â Ø�;@?; b �@1a�A6 � f % �* d

ã �

�}ê

Page 23: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

��� � ��� ����������������� �

/OØ�;'?�:<ßTÝ $ � ê��������5�!� EF?I= � ( Ú � � �TY � LJ?�AMØ<=K?#=KÝJ? $ =@Ý ÜJ;>Ø(�>?�ß7=KCFØ<A àË:<ÜJÜJCGAJ� LJ?7ÛèOAJ?IL�:\Ù � ( �=� = �������5�\��(����������B� � % � ��(+:\AJL�HeÖ � = ('Ú �

� �TY � ( Þ � = ( �=� = �������5�\��(����������B� ��% ��Z� = ���������\��("%�=KÝJ?�ÜM;@Ø(�>?IßI=KCGØ�A Ø â �

� Ø�Ae=KØgCh=KÙ%èO;>Ù>= $ ßIØ�àËܹØ�AJ?IAe=KÙ�ã <�A$=@ÝJ?�Ù@? +r�J?�EO×R?�×�CGEFE}�M=KCGEFCG��?=KÝJ? â Ø�EGEFØ_×�CFAM� â :<ßI=@Ø�;@CG��:\=@CFØ�A+EG?�àÈà3:�=@ÝJ?gÜJ;@Ø}Ø â Ø â ×�ÝMCFßTÝ�ß�:<A�H ? â Ø��MAJL�CGA�é :<AMÙ@Ù@EG?�; � �}=@�M=K?�tê_ì"2"2VÞJܧãhê_ì">VÞ8�M:\=@� #}ã Mã �VêD%�:\AJL - ;@AMØ�EFL1�tê�ì�ì">MÞJÜyã � MÞ �M:\=@� ê�ã �Jã "%7ã�M������� �� D$< ��� = ��� = % W6D�Aa9�DVA�587:@BACW�I�D�5 ;�A 08DqA4TQ �=� t ��� �=� t %B% WCDqA �P2$I+*K5S]`5 ;�A�08D D �C7:* ;6;[D8Q ��* <=]* <�5�� 2�@VDBI+*�A�4 � ��.bI-ECDW�@FA�ECDF4TDB@FAC<XD3QjWVGo<=]TDs2V;�DF4>587�W�5VD�<=5�2$O � t _ n!]TDB4�OZ2�@�D\A�0^]�;l@\2 W A6W�*+IK*Z<-G9RD\A�5?7�@VD � = t 2$4><=]TD�;l@V2 Q&7 0�<!5Z;�A�08D �=� = V�� t ��� = � ��� t %)% <=]TDF@VDbD�� *K5?<�5eAq<=@BA465�*Z<=*�2�4�;l@\2 W��A6W�*+IK* <-G � t Ú � = V � �=� t % �TY . 3���ê�1 A4TQfAs9fA�@SE *+4 A�I�;l@\2 W A6W*KIK*Z<-G � = Ú�� = �TY . 3���ê 1 5?7�0^]j<�] AC<2$4TDp] A�5 <�]TDpO�A�0$<�2$@�* ��AC<�*�2$4

� = t � %�� 3� �3� ûê���� = �� t % � t �� = ��I t % � = �KI� = %&� ���<ì$%

OZ2$@qD\A�0^] 9RD\A�5?7�@BA6W�I#D % � = � �=� t %V_ n!]TD�9�DVA�587:@VD=� = 2$4 ��� = ��� = % *K5JQ6D �64TD3Q WVG <=]TD;l@V2 �8D80$<�*�2$4�9fA8;6;T*K4CE � = Ú � = VR� t �lY � = � � = �� = �� t %��� = 5?7�0^]j<�] AC<%� = � � = � ÚT� ��� � Y == _n!]TDbO�A�0$<�2$@�* ��AC<�*�2$4 *+4 )�� �8, *+5 � = t �PA _ 5 _ 7:46* �67�D _��Ø�:<ÜJÜJEhÖ åa?�àÈà3: #'×R?ËèO;>Ù>=�Ù@ÝJØ_× =KÝO:Ê=·=@ÝJ?ËÙ>ÜO:<ßI? � � F BGHG V F BG CFÙ���Ø�EGCFÙ@Ýyã /OØ�EFEGØd×�CGAJ�C�:<�J?I;��Yê_ì�ì��}ÞcÜyãGêD2\ìMÞ CR?�CFÙ>ÜJCF?IEF?'êIÛ �A%7Þa=KÝM?3ä��JßIEFCFLM?�:<A Ù@ÜO:\ß�? F B CFÙ ��Ø�EGCFÙ>ݧÞ�ÝM?�AJßI? F BGHG :<AMLF BG H¹?�CGAJ�+Ø�ܹ?�A#:\AJL�ß�EGØ�Ù@?IL�Ù@�JHJÙ>ÜO:<ßI?�ÙgØ â : ��Ø<EFCFÙ>Ý�Ù@ÜJ:<ß�?$:<;>? ��Ø<EFCFÙ>Ý�:<AJL�ÝM?�AJßI?$:<EFÙ>Ø3=KÝJ?ICF;ÜJ;@Ø}LJ�Jß7=�ã ��ÝJCGÙÆÙ>ÝJØ_×�ÙÆ=@ÝO:\=�=@ÝJ?gÙ@ÜO:<ßI? � ÙK:\=@CFÙtèO?�Ù�=KÝM?6;>?�+r�JCG;@?�àÈ?�Ae=@ÙÆØ â åa?�àÈà3: #}ã��ÝJ? LJ?IÙ@CF;>?�L â :<ß7=KØ�;>CF��:\=KCGØ�A �Yê�êD%�Ø â =KÝJ?ÉàÈ?�:\Ù@�J;>? � CFA - Ù@Ù>�JàËÜV=KCFØ<A«ê CFÙDAJØ_× :\ßTÝJCF?7á�?�L#HeÖ�:;@?IÜ ?�:\=K?IL«:<ÜJÜMEFCFß�:\=KCGØ�A�Ø â åa?�àÈà3:6#Vã <�A�:"èO;@Ùt=·Ùt=K?IܧÞ��MÙ@CFAM��=@ÝJ?$AJØ<=T:Ê=KCFØ<A�Ø â åa?IàËàË:6#VÞÏÙ@?I=� = � � ��Y = Þ � t � � :<AML � = t � � =@ØÈØ<HM=T:<CGA"=KÝJ? â :<ß7=KØ�;>CF��:Ê=KCFØ<A

� � � % � 3 5 7 � � 3 5%ê � �Z� ��Y == �B� ��% � �@�Z� ��Y == ��I ��� % � ��Y = �KI ���Y == %

â Ø�;%?�:<ßTÝ àÈ?�:<Ù>�J;K:<HMEF? � % � � � � %a×�CG=@Ý :D=K;@:<AJÙ>CG=KCGØ�A6ÜJ;@Ø�HJ:<HJCFEGCG=�Ö � �ÍÚ � ��Y = Vb� � � %��TY . 3 ��ê 1:<AJL�: à3:<;>��CFAJ:<EyÜJ;>Ø�HO:<HMCFEFCh=�Ö � ��Y = � � = ��Y = � ÚT� ��� � Y == ��Y = ã<�A :"Ù>?�ß�Ø<AJL Ùt=K?�ÜyÞcÙ>?I=s� = � � ��Y t Þ!� t � � :<AJL � = t � � ��Y = =@Ø'Ø�HM=T:\CFA : â :<ßI=@Ø�;@CG��:\=@CFØ�A�Ø â� ��Y = CFAe=KØ6=K;K:\AJÙ@Ch=KCFØ<A3ÜJ;>Ø�HO:<HJCGEFCh=�Ö � ��Y = Ú �

��Y t V � � � % �TY . 3���ê�1§:<AML+à3:\;@��CGAO:<EOÜJ;>Ø�HO:<HJCGEFCh=�Ö� ��Y t � � = ��Y t � ��Y = ÚT� � ��Y = � �Y == ��Y t ã�æqØ�Ae=@CFAr�JCFAM�ÆCGA1=KÝJCGÙ â :<Ù@ÝJCGØ�AgØ�AJ?,Ø�HM=K:<CFAMÙÏ:�Ù>?�+r�J?IAJß�?�Ø â=K;@:<AJÙ@Ch=KCGØ�AgÜJ;@Ø�HJ:<HJCFEGCG=@CF?�Ù � (MÞ $ � � �������5� �Æ:\AJL�àË:<;@�<CFAO:<E\ÜJ;@Ø<HO:<HJCGEFCG=@CF?IÙ � (MÞ $ � �h�Èê��������5��ê�ã

- =3?�:<ßTÝÍÙt=T:<��? $ � ê�=KÝJ?�àË?�:<Ù@�M;@? � (�CFÙ â :<ßI=@Ø�;@CG��?IL CFAe=@Ø :#=K;K:\AJÙ@Ch=KCFØ<A ÜM;@Ø�HO:\HJCFEGCG=�Ö � ( Ú� (ZY = Vo� � � %j�&Y . 3���ê�1�:<AMLç:�àË:<;@��CGAO:<E�ÜJ;>Ø�HO:<HMCFEFCh=�Ö � (yY = � � = (yY = � ( ÚC� � ( � � Y == (ZY = ã*<�A=KÝJ? èOAJ:<E�Ù>=@?�Ü Ø�AJ?$Ø�HM=K:<CFAJÙ0: â :\ßI=KØ<;@CF��:\=KCGØ�A�Ø â =KÝM?ÈàÈ?�:\Ù@�J;>? � t CGAe=KØ"=K;@:<AJÙ@Ch=KCGØ�A�ÜJ;>Ø�HO:<HJCGEFCh=�Ö� t Ú � V�� � � %��lY . 3 ��ê 1Ï:<AML�àË:<;@��CGAO:<E¹ÜJ;@Ø<HO:<HJCGEFCG=�Ö � = ×�ÝJCFßTÝ�ÙK:Ê=KCFÙtèO?�Ù � = � � = � ÚT� ��� � Y ==ß�Ø�àÈÜJEG?I=KCGAJ�É=KÝM?6ÜM;@Ø}Ø â Ø â åa?�àÈàË: �Jã �

� �

Page 24: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

����� ��� ����������� � � �� � �

�vC % 5�=KCGEFCF�ICFAJ�0=@ÝJ?ÆÜJ;@Ø�ܹ?�;t=KCG?�Ù�Ø â =KÝM?Dá\:<EF�M? â �MAJßI=@CFØ�A ; = Ù>=T:Ê=K?�L3CFA �,;>Ø�ܹØ�Ù@Ch=KCFØ<A�ê|:<AJLÈ=KÝJ?DAJØ�AVÛ;@?ILJ�JAJLO:\AJßIÖ�Ø â =KÝJ?�àË?�:<Ù@�J;>? � = Ùt=T:\=@?�L�CGA - Ù>Ù@�JàÈÜM=KCGØ�A � ��CFC %�=@ÝJ?ÉÜJ;>ØVØ â CFÙ|Ùt=K;@:<CF��Ýe= â Ø�;>×q:<;@LHeÖ â Ø�EFEGØd×�CGAJ�ÉÙt=K?�ÜMÙ6ê � CFA"=@ÝJ?gÜJ;@Ø}Ø â Ø â ��;>Ø�Ü Ø<Ù@CG=@CFØ�A�ê<ã�vCGC %E/OØ�;$?�:<Ù>?�Ø â AJØ<=K:\=KCGØ�A ×R?�Ù>ÝO:<EGE�:<LJØ�ÜM=È=KÝM? â Ø�EGEFØ_×�CFAM��ß�Ø�Aeá�?IAe=KCFØ<AJÙ�ã /OØ�;È:<AeÖ Ù>=K;@:\=K?I�<Ö� L � g % %

B�@1a�A6 � f %%×q?ÆÙ@?7=hN!( �Z� ( = %�ÚT� N b_Þ`W�( �=� ( = %�ÚC�gW�b�:<AJL � �@W�(yY = �Z�

(ZY == %&�\��( �\�'�(�� �1,(ZY = %qÚT�f C â $ � 3D:<ÙÏ×R?�EFE}:<Ù �1zbÆÚC�g1 :<ÙcH ? â Ø�;@?\ã � ?�ß�:<EFE â ;>Ø�àµë0?IèJAJCG=@CFØ�A ��=KÝO:\=c=KÝM?�=@?�;@àÈCFAJ:<E�ÜJEF:<A·Ø âm ��� â ?�:<Ù@CGHJEF?�Ù>=K;@:\=K?I�<Ö�Ù@:\=KCGÙ>èO?IÙ�N5�@�Z� � = %,� � �@W���Y = �Z�

��Y == %&�\��� �\�'�� � �1���Y = %0:\AJL#W�� �=� � = % � 3�� � = % � � ã é1CGá<?�A =@ÝJ?'Ø�ÜM=@CFàË:<E�LJ?Iß�CFÙ>CFØ�A �=N � b �!W �b % â ;>Ø�à �vC %É:<AJL =KÝJ? â �JAJß7=KCFØ<AJÙ �=N � ( �!W �( %�� i %LJ?IèJAJ?�L'CFA?��;@Ø�ܹØ�Ù@Ch=KCGØ�A�ê �vCFCGC %%EG?I=q=@ÝJ?|Ùt=K;@:\=K?I�<Ö�� L � � g � %,H ?0LM?IèOAJ?IL':<ÙqCGA �vCGC %kØ â ��ÝM?�Ø�;>?�à)ê:<AJL"Ù>?I=kN � ( � f (`�\� ( = %�ÚT� N � b :<AJLtW �( � f ( �\� ( = %�ÚT�gW �b C â $ � 3Mã�/%CGAO:<EGEGÖ�Þe;>?�ß�:<EFE â ;@Ø�à =KÝM?|LJ?7èOAJCG=@CFØ�A�tê �4%qØ â =@ÝJ?1á\:<EF�J? â �MAJßI=@CFØ�AJÙ/;8(MÞ $ �&ê��������&�!� ÞJ=KÝO:\= â Ø<;�?�:<ßTÝ��f )*� ���(È:<AJL>� ( = %�� (

;H( � �f �\� ( = %��+& �=N � ( �_�f �\� ( = %)% - ( 3 5 ;8( G = � � �@W �( � �f �B� ( = % �\���\�'�( G = � �1,($% �\� ( = �\�D% � ( G = �=�(= �!I �D%&� � "3$%

åa?I=�� �L � �g %�� �&�N b����N = � i %&�����������N&�@� i % � �W�b�� �W = � i % �������&���W�� � i %B% % B�@1a�@6 � f %�H ?g:<A�:<;>HJCG=@;K:<;tÖ3Ùt=K;@:\=>Û

?��<Ö<ã=��ÝJ?�ßIEÑ:<CGà ×�CFEGE â Ø�EFEGØ_× C â ×R?�Ù@ÝMØd×µ=@ÝO:\= ,�-/.@* bD� L � � i %A1 ):,?- � * b(� �L � i % � ã=< â � �Çê�ÞO=@ÝJCFÙ=T:<ÙB�#CFÙg=K;@Chá}CÑ:<EkÙ>CFAJßI?+:<AeÖ Ù>=@;K:\=@?��<Ö ;>?�LJ�JßI?�Ù�=@Ø�:�LJ?�ßICFÙ@CGØ�A â Ø<;j�J� 3�:<AJL =KÝJ?ËCFAJ? +}�J:<EFCh=�Ö�CFÙ=KÝJ?I;@? â Ø�;@?ËCFàÈÜJEFCG?�L#HeÖ;��C %7ã�BÆ?�AJßI?3=KÝJ?Ë;@?Ià3:<CGAJLJ?I;�:<Ù>Ù@�JàÈ?�Ù·=KÝO:\=c� ) �Vã6��ÝJ?+CFLM?�:�Ø â =KÝJ?ÜJ;@Ø}Ø â CGÙc=@Ø|ßIØ�AJÙ>=@;@�Jß7=�:ÆEFCFÙt=cØ â CFAMLJ�Jß�?ILÉÙ>=@;K:\=@?���CG?�Ù � �L ; ( ? � �g ; ( ? %Þ $ �&ê��������5�!���Èê�Ø�HM=K:<CFAJ?IL·HeÖÙ@�JßIß�?IÙ@Ù@Chá�?IEGÖ�;>?�ÜJEF:<ß�CGAJ�Ë=@ÝJ?�ÜMEÑ:<AJÙE�&�N!(��`�W�($% � i %�CFA � �L � �g %�×�CG=@Ý�=KÝJ?·Ü Ø\=K?�Ae=@CÑ:<EGEGÖ"Ø�ÜV=KCFàË:<EaÜJEF:<AJÙâ Ø�;qÙt=T:<�<? $ LJ?7èOAJ?IL�HeÖË=KÝJ? â �MAJßI=@CFØ�AJÙ �=N � ( ��W �( % � i % â ;@Ø�à ��;@Ø<Ü Ø�Ù>CG=@CFØ�A�ê �vCGCFC %k:\AJL+=KØÉÙ>ÝJØ_× =@ÝO:\=

,�- .0* bD� L � � i %A1 ) ,?-� *�b(� �L ;>=@? � i %�7)*�����8) ,?-� *�b(� �L ; ��Y =@? � i %�7) ,?-� *�b(� �L � i %�e� � MêD%

/OØ�EFEGØd×�CGAJ� =@ÝJ? :<H Ø_á<? ßIØ�Aeá�?IAr=@CFØ�AMÙ�ÞgLJ?IèJAJ? â Ø�;'?�:<ßTÝ Ù>=K:<��? $ � 3���ê��������5��� =@ÝJ?#CFAJLM�Jß�?ILÙ>=@;K:\=@?��<Ö � �L ; ( ? � �g ; ( ? %�� �&�N ; ( ?b ���N ; ( ?= � i % �������&���N ;

( ?� � i %&�`�W ;( ?b �`�W ; ( ?= � i % �������&���W ;

( ?� � i %B%�:<Ù â Ø�EFEGØ_×�Ù�Ú�N�; ( ?" �Z� " = % ÚT� �N "@�Z� " = % � / � 3���ê��������&� $ � ê�W`; ( ?" �Z� " = % ÚT� �W " �Z� " = %&� / � 3���ê��������&� $ � ê�N�; ( ?" �Z� " = % ÚT� N � " � � � �W`; ( ?"�Y = �Z�

"�Y == %&�\� " �\�' " � �1/"�Y = %&�\�"= % / � $ ���������!�

�W`; ( ?" �Z� " = % ÚT� W �" � � � �W\; ( ?"�Y = �=�"�Y == %&�B��" �l�' ",� �1/"�Y = % �\�

"= %./ � $ ���������!� �

� ��"%

� HJÙ@?I;>á�?�=KÝO:Ê=%?�:<ßTÝ�Ùt=K;K:Ê=K?��\Ö � �L ; ( ? � �g ; ( ? %§CGÙ â ?�:<Ù@CGHJEF?,:\AJL�ßIØ�CFAJßICFLJ?IÙa×�CG=KÝg=KÝM?RØ�;>CF��CGAO:<E\Ù>=K;@:\=K?I�<Ö� �L � �g %k�JÜ$=KØ6Ü ?I;@CGØVLÈÙ>=K:<��? $ ��ê ��=@ÝJ?DÙ@:<àÈ?ÆCGÙ,Ø�HeáVCGØ��JÙ>EGÖÉ=@;@�J? â Ø�;�:<AeÖ$Ù>=@;K:\=@?��<Ö � �L ; " ? � �g ; " ? %×�CG=@Ý / � $ %ã <�A ÜO:<;t=KCFßI�JEÑ:\;�Þ|=@ÝJ? Ùt=K;K:Ê=K?��<CF?�Ù�CFAJLM�Jß�? =KÝJ?�ÙK:<àÈ? ×R?�:\EG=KÝ ÜJ;@Ø}ß�?IÙ@Ù��JAe=@CFEÙ>=K:<��? $ :<AJL ÝJ?�AMß�?�Ö}CF?IEFL =KÝJ?�ÙK:<àÈ?�;K:<AJLMØ�à á\:<;@CF:<HJEF? � � �W�(ZY = �=�

(yY == %&�B��( �l�'�( � �1,(yY = %$LM?IèOAVÛCFAJ�È×q?�:<EG=@Ý#:\=0Ùt=T:<�<? $ ã /�;>Ø�à Ù>=K:<��? $ Ø�Ae×�:<;>LJÙ|=@ÝJ?ÉÜJEF:<AJÙ|Ø â =KÝJ?�Ù>=K;@:\=K?I�<Ö � �L ; ( ? � �g ; ( ? %Æ:<;@?LJ?IèJAJ?�LÍHeÖ =KÝM? â �JAMßI=KCGØ�AJÙ*�)��N � " �!W �" %�� i %)% �" �( ã � HJÙ>?�;>á<?<Þ�ÝJØ_×R?Iá�?I;�Þ�=KÝJ:\=Ë=@ÝJCFÙ$LJØ}?�Ù �<xyo CFà ÛÜJEGÖ�=@ÝO:\=�� �L ; ( ? � �g ; ( ? %1ß�Ø<CFAJßICFLJ?IÙ6×�Ch=KÝ;� �L � � �g � % â ;@Ø�à Ùt=T:<��? $ Ø<Ar×q:<;>LJÙÉH¹?�ß�:\�JÙ@?ËCFA �<?�AJ?I;K:<E� � �W�(ZY = �Z�

(ZY == % �\��(��l�'�(�� �1 (ZY = % �� � �KW �(ZY = �=�(yY == %&�B��( �l�'�(`� �1,(yY = %7ã�

Page 25: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

�VCFAMß�?k=KÝM?,:<H Ø_á<?�ßIØ�Aeá�?IAr=@CFØ�AMÙcCGàËÜMEGÖ�=KÝO:Ê=�� �L ; � ? � �g ; � ? %�� � �L � �g %§:<AJL�� �L ; b ? � �g ; b ? %�� � �L � � �g � %7Þ=KÝJ?·ß�EF:<CFà � MêD%�×�CFEGE â Ø�EFEGØd× C â ×R?�Ù>ÝJØ_×�=KÝO:\= ,�- � * b(� �L ; ( ? � i % ):,?- � * b(� �L ; ( G =@? � i % â Ø<;D?�:<ßTÝ$ � 3��������5�!�*��ê<ã �VCFAMß�?�HeÖ$LJ?IèOAMCG=KCGØ�A �� ��4%�=KÝJ?�Ù>=@;K:\=@?���CG?�Ù � �L ; ( ? � �g ; ( ? %�:<AJL*� �L ; ( G =@? � �g ; ( G =@? %ß�Ø�CGAJß�CGLJ?1�JAe=KCGE§Ù>=K:<��? $ �Íê�ÞOCh=�Ù@���ÈßI?�ÙD=@Ø$Ù@ÝJØ_× =@ÝO:\= â Ø�;�?�:<ßTÝ $ � 3 �������5�!� � ê

,�-�� �'"� �( (" Y\( & �&�N ; ( ?" � i %B%�� ) ,?-�� �'"� �( (

"�Y\( & �&�N ; ( G =@?" � i %)%���� � $%

� � �1' - Ù>Ù@�JàÈ?�=KÝO:Ê= $ � 3Mã åÏ?7=>� ( = % � ( H¹? :<;@HJCh=K;@:<;>Ö HJ�M="è &V?IL :<AML Ù>?I= �f ( ÚT�� � �W�(ZY = �Z�

(ZY == % �\��(��l�'�(�� �1 (ZY = %�) � �� (Mã � ?�ß�:\EFE â ;@Ø�à � ��"%g=@ÝO:\=6=KÝJ?3Ù>=K;@:\=K?I�<Ö � �L ; ( ? � �g ; ( ? %gCFÙLJ?IèJAJ?�L#HeÖ'=KÝJ? â �MAJßI=@CFØ�AJÙE�)��N � " �!W �" %�� i %)% �" �( â ;@Ø<à Ù>=T:\��? $ Ø<Ar×q:<;>LJÙ�ã 5ÆÙ@CGAJ�3=KÝM?�ß�Ø<AJLJCG=@CFØ�AJ:<ELJCFÙt=K;>CFHJ�M=@CFØ�AMÙ � "DÞH/ � $ - ê������������ â ;>Ø�à5åa?IàËàË: �È:<AJL�?�+r�O:\=@CFØ�A1�� 43$%R=KÝJCGÙ�CFàÈÜJEFCG?�ÙR=@ÝO:\=

3 5 ����� 3 5 �'"� �( (" Y\( & �&�N ; ( ?" �=� " = %B% � � �=� ��Y == �!I ��� % i�i�i � ( G = �Z�

(= �!I ��( G = %��4;H( � �f (`�\� ( = %&� � �A%

åaC,�<?7×�CFÙ>?<Þ â Ø�;�:<AeÖËè &V?IL>� ( G == %�� ( G = :<AJL �f ( G = ÚT� � � �W�( �Z� ( = %&�\��( G = �`�'�( G = � �1,("%�)*� ���( G = =KÝJ?ÜJEÑ:\AJÙ�Ø â Ùt=K;@:\=K?I�<Ö � �L ; ( G =@? � �g ; ( G =@? %�ÙK:\=@CFÙ â Ö

3 5 ����� 3 5 �'"� �( G = ("�Y\( & �&�N ; ( G =@?" �Z� " = %)% � � �Z� ��Y == �!I � � %<����� � ( G t �Z� ( G == �!I ��( G t %�� ( ;8( G = �_�f ( G = �\�

( G == %&�� $#"%

æqØ�àÉHJCGAJCFAM�F�� �$%y:<AJL �� "#"%y:<AJLg;>?�ß�:\EFEFCGAJ� â ;>Ø�à � ��"%¹=@ÝO:\= �N�; ( G =@?( �=� ( = %�� �N!( �Z� ( = %§:<AJL��W`; ( G =@?( �=� ( = %���W�( �=� ( = %�Ø�AJ?gÝO:\Ù â Ø<;�?�:<ßTÝ'è &V?�L��

(= %�� (

3 5������ 3 5 �'"� �( (" Y\( � & �&�N ; ( ?" �=� " = %)%�� & �&�N ; ( G =@?" �Z� " = %)% � � �@�=� ��Y == �!I ��� %<����� � ( G = �Z�

(= ��I ��( G = %

� ;H( � �f ( �\� ( = %�� & �&�N!( �=� ( = %B%�� ( 3 5 ;H( G = � � � �W�( �Z� ( = %&�\���l�'�( G = � �1 ($% �\� ( = �\�D%B% � ( G = �=�(= �!I �D%e):3��

� "!$%

×�ÝJ?�;>?3:\Ù6H¹? â Ø<;@? �f ( � � ���W�(ZY = �=�(ZY == % �\��(��l�'�( � �1,(yY = %7ãËæqEG?�:<;>EGÖ�Þ � "!$%|ÝJØ�EGLJÙ0×�CG=@Ý�? +r�O:<EFCh=�Ö�C â

:<AJL�Ø�AJEGÖ+C â �N ( �Z� ( = % � N � ( �_�f (��B� ( = %�:<AJLs�W�( �=� ( = % �*W �( �_�f ( �B� ( = %7ã 5DÙ>CFAJ�$=KÝJ?6AJØ<=K:\=KCGØ�A'CFAe=K;>ØVLM�Jß�?ILCFA#=KÝJ?$ÜJ;>ØVØ â Ø â åÏ?IàËàË: ��EG?I= � (#ÚC� � = ( � LJ?�AJØ\=K?$=KÝJ? �>Ø�CFAe=6àË:<;@��CGAO:<E�LJCFÙt=K;@CGHJ�M=@CFØ�A�Ø â =KÝJ?;K:<AMLJØ�à-á\:<;@CF:<HJEG?�Ù � = �������5�\��(}ã���ÝJ?3CGAJ?�+r�O:\EFCG=�Ö�CFA �� "!"%1H¹?�CGAJ�'=K;@�M? â Ø�;·:<EGEP� ( = % � ( CGàËÜMEFCF?IÙ=KÝO:Ê=�CG=RCFÙRÜJ;@?IÙ@?I;>á�?IL��MAJLJ?�;qCFAe=K?I��;K:\=@CFØ�AÈ×�CG=@Ý3;@?IÙ@ܹ?�ß7=�=KØ � (Mã��3BÆ?�AJßI?<ÞJCGAe=K?��<;K:\=@CFAJ�·H Ø<=@Ý+Ù@CGLJ?�Ù� 2 7K0'!/%'*-# 0'(|zV!/7:W8@e48*�!AHZ4VY�7:, (:*V0'!/`V%'#&0[! � n8l � Q[Y-H2HZ!2Q'Q[(|zV!/7:W 4BzV!/%a0[>�! H/48*-,1(+0[(:48*_#&7 ,1( Q�0'%[(:.�Y10'(+4V*-Q ���� � � �� �#8*-,$0[>�! ?)#8%[`V(+*-#87 ,1(:Q 0[%'(:.�Y10[(:48*�� y ,�!X�-*�!�, (+*���!2? ?)#Jf_\

���

Page 26: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

Ø â �� "!$%R×�Ch=KÝ';@?IÙ@ܹ?�ß7=D=@Ø � (È:<AJL�?'&VÜJEGØ�CG=@CFAJ��=@ÝJ? â :<ßI=@Ø�;@CG��:\=@CFØ�A'åa?IàËàË: �$��CGá<?�Ù

,?- � �'" �( ("�Y\( � & �&�N ; ( ?" � i %B%�� � ,�-�� �'"� �( (

" Y\( & �&�N ; ( G =@?" � i %B%��� 3 5 � 3 5 ����� 3 5

�'"� �( (" Y\( & �&�N ; ( ?" �=� " = %B% � �@�=� ��Y == �!I ��� % i�i�i � ( G = �Z�

(= �!I ��( G = % � ( �@I � ( = %

� 3 5 � 3)5 ����� 365�'"� �( (

" Y\( & �&�N ; ( G =@?" �=� " = %B% � �@�=� ��Y == �!I ��� %<����� � ( G = �=�(= �!I ��( G = % � ( �@I � ( = %

� 3 5 � ;H( � � � �W�(yY = �Z�(yY == %&�\��( �\�'�( � �1,(ZY = %&�\�

(= % � ( �KI � ( = %�� 3 5 � & �&�N!( �=� ( = %B% � ( �@I � ( = %

� ( 3 5 ;H( G = � � � �W�( �Z� ( = %&�\���l�'�( G = � �1 ($% �\� ( = �\�D%B% � ( G = �=�(= �!I �D% � ( �KI � ( = %e):3��

��ÝJCFÙ�ÜJ;>Ø_á�?�Ù �� $% â Ø�;�=KÝM?6ß�:<Ù@? $ � 3Mã� � � � - Ù@Ù>�JàË?'=KÝJ:\= $ � 3Mã <�A =KÝJCGÙ ß�:<Ù>?<Þ�Ø<AJ?�ÝJ:<Ù � �L ; b ? � �g ; b ? %0� � �L � � �g � % :<AJL =KÝJ?Ù>=@;K:\=@?���CG?�Ù�àË:_Ö3Ø�AJEhÖ3LJC �y?I;q×�CG=@Ý";@?IÙ@ܹ?�ßI=�=@Ø$=@ÝJ?1LJ?Iß�CFÙ>CFØ�AMÙ �=N � b �!W �b %�:<AML �&�N�; =@?b � �W`;>=@?b %�� �&�N&b����W�b.%7ã5DÙ>CFAJ��:\A :<AO:<EGØ���Ø��JÙ6;@?�:<Ù@Ø<AJCFAJ��:<ÙÉCFA =KÝJ?3ÜJ;@?7áVCGØ��JÙÉß�:<Ù@?"Ø<AJ?3ÝO:\Ù â ;@Ø�à �� 43$%6:\AJL �� ��4% â Ø�;?�:<ßTÝ�è &V?�L>� = %c�365 ����� 3)5 �'"� = (

" & �&�N ; b ?" �Z� " = %)% � � �Z� ��Y == �!I ����%<����� � t �=� = �!I � t % � ( ; = � � �KW �b �\� = �l�' = ��1F%&�\� = %

365 ����� 3)5 �'"� = (" & �&�N ;>=@?" �Z� " = %)% � � �Z� ��Y == �!I ����%<����� � t �=� = �!I � t % � ( ; = � � � �W�b��\� = �`�' = �!1F% �\� = % �

BD?IAJß�?6Ø�AJ?gØ�HM=K:<CFAMÙ�ÞJ�M=@CFEGCF��CGAJ�·=@ÝJ? â :<ßI=@Ø�;@CG��:\=@CFØ�A'åa?IàËàË: �

,?- � �'"� 8b (" & �&�N ; b ?" � i %)% � ��,?- � �'"� 8b (

" & �&�N ; =@?" � i %)% �� 3 5 3 5 ����� 3 5 �'"� 8b (

" � & �&�N ; b ?" �=� " = %B% � � �=� ��Y == �!I ��� %<����� � t �Z� = ��I � t % � = �KI � = %� 3 5 3 5 ����� 3 5 �'"� 8b (

" & �&�N ; =@?" �Z� " = %)% � �@�Z� ��Y == �!I � � %<����� � t �Z� = �!I � t % � = �@I � = %� & �=N � b % - ( 3 5 ; = � � �@W �b �\���\�' = �!1F% �\� = % � = �@I �D%�� & �&�N b.%�� ( 3 5 ; = � � ���W�b��\���l�' = ��1F%&�\� = % � = �@I �D%) 3��

×�ÝJ?�;>?·? +r�O:<EFCh=�Ö+ÝJØ<EFLJÙ�C â :<AML�Ø�AMEGÖ+C â �&�N b����W�b'%�� ��N � b ��W �b %7ã�vCGCFC % ��ÝJCFÙ�CGÙ�:<A'CFàÈàË?ILJCÑ:\=@?|ßIØ�AJÙ@? +r�J?�AJßI?ÉØ â =KÝJ?gEF:<Ù>=�Ùt=T:\=@?�àÈ?�Ae=�ã �

�4#

Page 27: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

��� � ��� ����������� � ��������� �� �

��ÝJ?6ÜJ;@Ø}Ø â �JÙ@?IÙÆ=@ÝJ? â Ø�EFEGØ_×�CFAJ�ÉEG?�àÈà3:�×�ÝMCFßTÝ�CFÙ�ÜJ;>Ødá<?�L�èO;@Ùt=�ã�M��������� D$< �� W6DbAH;T@V2 W ACW�*KI+* <-Gf9RD\A�5?7�@VDU2$4 � � ��� � � %B% 5?78;6;�2�@?<XD3Q/2�4 <=]TDU032$9�;�A�0$<�5\D$< �� � � ��]6*#0^]*K4TQ 7 08DF5U4T2$4 ��@VD8Q 7:4TQ A�4&<kA�5S5VD�<=5�*K4 <�]TD�5\DB465\Dq2�O sD �646*Z<=*�2�4�� _ � * d$DF4 dVA�I 7 DF5 �� ) 3�� �1 � 3��f �9��� � �1 ��6 � 3 A�4TQ �( � 3 I!D�< � Ú � �&Y F GHG WCDk5V2$9�Db032$4&<=*+4T7�2 7:5hOX7:4&0$<=*#2$4aA�4TQfQ6D��64&D& � i �(� % A�5k*K4R.b5S5?7:9s;[<=*#2$4 � _ n!]TDB4j<=]&Db5\2$I 7C<=*�2�4 <X2 <=]TDr;l@\2 W�I�DF9

à3:(&; � � � ?� � - � -�� < & ��N � � % - �( 3 5 & � . �1�[ - �� -�]��x� 1 � �=�(%�� � � �� �@I �D% BBB N<-�[ -N] D 60� f ��[ )*��� � �1 C

� $2"%*K5�7:4C*�C7 DBI GcQ6D �64TD8QRA�4TQ�< A���DB5 <=]&DbOZ2�@�9

N � � �N � f - �� � �1 �l�] � � �tê � �N % � f -*�� � �1 � & �[ � � �tê � �N % � f -*�� � �1 �A�tê ��6 D & � % � �� � �1J�

� ">$%

��]TDB@\D �N � � ê -�� � ���� � � Y = A�4&Q& � ÚC� :<;@��à3:D&! � � < 3)5 & � . �1��Yê���6 D &"% -)&�� �D%A1 � �=�D% � � � �� �KI �D% BBB & D 6 ê C � � �ì$%

� � ÚC��� � �( � � 3

�DàË:(&! � � < �( 3 5 & � . �1 �tê �N6 D &"% -'&�� �D%21 � �Z�D%�� � � �� �@I �D% BBB & D 6 ê)C � �� 3� �$3$%

���$%�%��É��? èO;@Ùt=6Ù@ÝJØ_×Ç=@ÝO:\=1=KÝM?$á\:<EG�J? & � CFA �� <ì$%|CFÙ0×R?�EGEhÛ�LM?IèOAJ?IL§ã�/OØ�;1?�:<ßTÝ & % � �:6 %·ÚT�� & %NF BG � 6 D & ê�"rÞMLJ?IèOAM?6=@ÝJ? â �JAJßI=@CFØ�A

*E� &�� �1a�A6 � �� % ÚT� 35 & � . �1��tê���6 D &4% -'&�� �D%A1 � �Z�D% �(� � �� �@I �D%&� � �JêD%

- ÜJÜMEGÖ}CFAJ�+åÏ?IàËàË:?>È=KÝJ? â �MAJßI=@CFØ�A *E� i � �1a�A6_� �� %DH¹?�CGAJ�3LJ?7èOAJ?IL Ø<A�=KÝJ?ÉßIØ�àÈÜO:<ßI=|Ù@?7= � �:68%DCFÙß�Ø�Ae=@CFAr�JØ��JÙ�CFàÈÜJEGÖ}CGAJ��=KÝJ?R?'&VCFÙt=K?�AMß�?�Ø â :DÙ@Ø<EF�M=@CFØ�Ag=KØE�� �ì$%ã 5ÆAJC,+r�J?IAJ?�Ù>Ùk×�CFEGE â Ø�EFEGØd×�C â ×q?RÙ@ÝJØ_×=KÝO:Ê=�*E� i � �1a�A6 � � %gCGÙ·Ùt=K;@CGßI=@EGÖ#ß�Ø<AJß�:�á�?\ã /OØ�;g=KÝJCGÙ·ÜM�J;@ܹØ�Ù@?\ÞkEF?7= & � & % � �L6 %1×�Ch=KÝ &� ���& Ñã�V?I=7W ÚC� �têv�~6 D & � & % % S :<AJL2W ÚT� �Yêv��6 D & � & % % S :<AJLçØ�HJÙ>?�;tá�?"=KÝO:Ê=�=KÝM?"AJØ�AVÛ;@?ILJ�JAJLO:\AJßIÖ#ÜJ;>Ø�ܹ?�;>=�Ö�Ø â =@ÝJ? àÈ?�:<Ù>�J;@?~�� CFàÈÜJEFCG?�ÙÆ=KÝO:\=1=@ÝJ? àÈ?�:<Ù>�J;K:<HMEF? Ù@?7= �KW �!W � �1F%6ÚT���� % ��� � �@W �\����3�� �1@% �� � �KW �\����3 � �1 % "'ÝJ:<ÙÉܹØ�Ù@Ch=KCGá<?3àÈ?�:<Ù>�J;@?\Þ�C±ã ?<ãhÞc�� � �@W �!W � �1F%)% � 3Mãä�àËÜJEGØ_ÖVCGAJ�$: Ù@CGàËCGEÑ:<;q:<;@���MàË?IAr=Æ:\Ù�CFA'Ù>=@?�Ü �$CGA+=KÝJ?gÜJ;>ØVØ â Ø â ��;@Ø�ܹØ�Ù@Ch=KCGØ�A�ê6:<AJL'?'&VÜJEGØ�CG=@CFAJ�=KÝJ?'EGCFAJ?�:<;@Ch=�Ö Ø â =KÝM? â �MAJßI=@CFØ�A � Ch= CFÙ AJØ_× Ùt=K;@:<CF��Ýe= â Ø�;>×q:<;@Lç=@Ø Ù>ÝJØ_×5=KÝJ:\= *E� � & - �Yêc�� % &� � �1c�A6 �`�� %�� � * � &�� �1a�A6 � �� % - �tê,� � % * � &� � �1a�A6 � �� % â Ø�;|:<EFE � % 1 3 ��ê�.¹ÜM;@Ø_á}CFAJ�3=@ÝJ?ÉÙt=K;@CGßI=ß�Ø�AMß�:�á}CG=�Ö"Ø â =@ÝJ? â �JAJß7=KCFØ<A�* � i � �1a�@6 � �� %ã���ÝJCFÙ�=@Ø���?I=@ÝJ?�;�×�Ch=KÝ+=@ÝJ?1ß�Ø�Aeá<?'&VCG=�Ö'Ø â =@ÝJ?1Ù@?7= � �:6 %

��!

Page 28: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

?�AJÙ>�J;@?IÙ·=@ÝJ?Ë�MAJC,+r�J?IAJ?�Ù>Ù�Ø â =KÝJ?ÈÙ@Ø<EF�M=@CFØ�A & � =KØ0�� <ì$%7ã <Ð= â Ø�EFEGØ_×�Ù0=KÝO:\=g=@ÝJ? á<:\EF�J? � � LM?IèOAJ?ILCFA � �$3$%�CFÙDCFAJLM?�?�L�×q?IEFEhÛÐLJ?IèJAJ?�L�:\AJL�ÙK:Ê=KCFÙtèO?�Ù � � � 3ËLJ�M?�=KØÈ=KÝJ?ÉÜM;@Ø�ܹ?�;t=KCF?IÙDØ â =KÝJ? â �JAJßI=@CFØ�A& � i �(� %ã%��?6ßIEÑ:<CGà =@ÝO:\=�=KÝM?gá\:<EG�J?�N � LJ?7èOAJ?IL�:<H¹Ø_á�?gÙK:\=@CFÙtèO?�Ù

N � � :\;@��à3:(&� � � � & �=N � � %_-)� � & � f - �� � �1U� N � � % BBB N f -*�� � �1 � � � � �"%

- ;>Ø��M=@CFAJ?$ß�:\EFß��MEÑ:\=@CFØ�A#Ù@ÝMØd×�Ù6=KÝO:Ê=·=@ÝJ?ËÙ>Ø�EF�V=KCFØ<A =@Ø � � �"%1CFÙgØ â =@ÝJ? â Ø<;@à N � � �N � f -}�� � �1 �×�CG=@Ý �N$H ?ICFAJ��LJ?IèOAM?�L :<Ù�:<H Ø_á<?<ã 9DØ_× EF?I=6=KÝM?Ëá\:<EF�M?�Ùj] � � � f - �� � �1 � N � � & � :<AML~[ � H ?LJ?IèJAJ?�L :<Ù1:\H Ø_á�?\ã1� ?ÉÙ>ÝJØ_× =@ÝO:\=0=@ÝJ?�=@;@CFÜMEF??�=N � ��[ � �^] � %ÆCGÙ|=KÝM?É�JAJC�+}�M?Éà3:D&MCGàËCG��?I;�=@Ø �� $24%7ã9DØ<=@?�èO;@Ùt=�=@ÝO:\=�3 d N � d f -2�� � �1 :<AJL[ � � f ��N � �c6HD<] � )*���� � �1Éã�BÆ?�AJßI?Æ=@ÝJ?�ß�Ø�AJÙt=K;@:<CFAe=KÙCFA1�� "2"%�:<;@?1Ù@:\=KCGÙ>èO?IL§ã�ë0?IèOAM?6=@ÝJ?1á<:\EF�J?

; � ÚC�:& ��N � � � %_- �( 3 5 & � . �1�[ � -*�� -�] � � � 1 � �=�D% � � � �� �KI �(% � � �� $%

åa?I=�� �Ny� �[ � �] % �� ��N � �^[ � �^] � %DH¹? :<AJØ<=@ÝJ?�;D=K;@CGÜJEF?6ÙK:Ê=KCFÙ â Ö}CFAJ� �N - �] D�6�- �[ � f :<AJL �[�) ���� � �1�ãë0?IèOAMCFAJ�

�;ÇÚT�+& � �N�� � % - �( 3 5 & � . �1 �[j-9�� - �]�� � 1 � �Z�D% � ��� �� �@I �D% � � �A%

×q?6Ù@ÝMØd× =KÝO:Ê=�; � � �;Ëã���ÝJ?6;@?�àË:<CGAJLJ?�;R=K;@?�:\=KÙ�=@ÝJ?gß�:<Ù>?�Ù � �� 3È:<AJL � � 3 Ù>?�ÜO:<;@:\=K?IEGÖ<ã� � �a' � �� 3Mã ��ÝJ?�LJ?7èOAJCG=@CFØ�AMÙ%Ø â ] � Þ & � :<AJL � � :\AJLÉ?�+r�O:Ê=KCFØ<A6� �� $%aCFàÈÜJEhÖ1=KÝJ?R;@?�EF:\=KCGØ�AJÙ>ÝJCFÜ; � � & ��N � �(� % - �( 3 5 & � . f - �� � �1s� N � 12. �1 �tê ��6 D & � % -'& � � �D%21 � �Z�D%�� ��� �� �KI �D%

� & ��N � �(� % - & � f - �� � �1U� N � � � � � �( 3 5 & � . �1 �Yê � 6 D & � % -)& � � �D%A1 � �Z�D% � � � �� �@I �D%� & ��N � �(� % - & � f - �� � �1U� N � � � � � � � � �A#"%

�V�JÜJܹØ�Ù>? �N2� f -��� � �1Éã ��ÝJ?�A =KÝJ?�HJ�MLJ��?I=�ßIØ�AJLJCh=KCFØ<AJÙ"CFàÈÜJEGÖ �[ � ��� � �1 :<AML �]}� 3Mãä�+}�J:\=KCGØ�AJÙ�� � �4%7Þ�� � �A%�:<AJL0� �$#"%R=KØ��<?I=KÝM?�;�×�CG=@Ý>N � �� �N|=KÝM?�A'ÖVCG?�EGL

�; �+& � �N�� � % � & � �N�� � % -�& � f - �� � �1s� �N � � % � �d & �=N � � � %_-�& � f - �� � �1s� N � � � % � � �4; � �

�V�JÜJܹØ�Ù>? �N d f - �� � �1Éã#ë0?7èOAJCFAM� �&«ÚT� . f - �� � �1U� �N 1 Y = �] :\AJLçØ�HJÙ>?�;>á}CGAJ��=KÝO:Ê= �& % � �:6 %��CGá<?�Ù

�; � & � �N � � % - �( 3 5 & � . f -*�� � �1s� �N 1 . �1 �Yê �N6 D �&4% - �&�� �D%A1 � �Z�D% � � � �� �@I �D% � �$!$%

� & � �N � � % - & � f -*�� � �1U� �N � � % ��×�ÝJ?�;>?

�� ÚC� � �( 3 5 & � . �1��tê���6 D �&4% - �&�� �D%A1 � �Z�D% �(� � �� �@I �D%&� � �A2"%

�42

Page 29: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

9DØ<=@? =KÝO:\=gØ<�J;6:<Ù@Ù>�JàËÜV=KCFØ<A � �Ny� �[ � �] % �� ��N � �^[ � �^] � %|CFàÈÜJEFCG?�ÙE� �N � �&"% �� �=N � � & � %7ã �V�JÜMÜ Ø�Ù>?ÈèJ;@Ù>==KÝO:Ê= ���;3Vã ��ÝJ?IAÈ? +r�O:\=KCGØ�A6� �"3$%c��Chá�?IÙ � � ) ��?��×�Ch=KÝÉÙt=K;@CGßI=�CGAJ?�+r�O:\EFCG=�ÖgC â �& �� & � %ãkä�+r�O:\=@CFØ�AJÙ� �A#4%�:<AJL0� �$!$%R=@ÝJ?�A�CFàÈÜJEhÖ

�; & � �N � � %_- & � f -9�� � �1s� �N �(� %#� � � �$>$% & �=N � � � % -�& � f - �� � �1s� N � � � % � � �4; �

×�CG=@Ý�:Ê=gEF?�:\Ù>=gØ�AJ?$CGAJ?�+r�O:<EGCG=�Ö�H ?ICFAJ�'Ùt=K;@CGßI=�ã��V?�ßIØ�AJL§ÞcÙ@�JÜMÜ Ø�Ù>? � d 3Mã ��ÝJ?IA ?�+r�O:Ê=KCFØ<A � �$3$%��CGá<?�Ù � � ��0��×�Ch=KÝ�Ù>=@;@CGßI=1CGAJ?�+r�O:<EGCG=�Ö�C â �& �� & � %7ã �VCFAJßI?É�M=@CFEFCh=�Ö'CFÙ0AM?��e:\=@CGá<?7ÛÐá\:<EG�J?�L�Ø<AJ?ÉÝO:<Ù& �=N � � % � � )�& ��N �(� % �� â Ø�;g?�:\ßTÝoN�) 3Mã � ?IÜ ?�:\=KCGAJ��=@ÝJ?$ÜJ;@?7á}CFØ��JÙ·:<;>���JàÈ?�Ae=�Ù>ÝJØ_×�Ù·=@ÝO:\=g=KÝJ?CFAJ? +r�O:<EFCh=�Ö � �$>$%�:<EGÙ@Ø ÝJØ�EGLJÙ�CFA"ß�:<Ù@?�� d 3Vã,BD?�AMß�? �; d ; � ã� � � � �3� 3Mã 9DØ<=@?R=KÝJ:\=%=@ÝJ?�H¹Ø��JAJLO:\;>Ö·ß�:<Ù>?�Ù �N � f -��� � �1 :<AML �N � 3|H¹Ø<=@ÝÉ��CGá<? �; �Q�

Ù@�JßTÝ#=KÝJ:\=1=K;>CGá}CÑ:<EGEGÖ ; � � �; CFA�=@ÝJCFÙ1ß�:<Ù@?\ã �V�JÜMÜ Ø�Ù>? =KÝJ?I;@? â Ø<;@?É=KÝJ:\= 3 d �N d f - �� � �1 :<AMLLJ?IèJAJ? �&$:<Ù�H¹? â Ø<;@?<ã <�A'=KÝJCGÙ�ß�:<Ù>?·? +r�O:\=KCGØ�AJÙ � �� $%�:<AJL0� �$#"%qà3:�Ö3H ?1×�;@Ch=@=@?�A�:<Ù

; � � & ��N � �(� % - �( & � f - �� � �1s� N � �(� �e- �( 3 5 & � . �1 �tê ��6 D & � % -'& � � �D%A1 � �Z�D% �(� � �� �@I �D%�; � & � �N � � %_- �( & � f - �� � �1U� �N � � � - �( 3 5 & � . �1 �Yê ��6 D �&"% - �&�� �D%A1 � �=�D% � � � �� �KI �D% �

� ?Iß�:<EGEFCGAJ� â ;@Ø<à � �$3"%�=KÝO:Ê= � � � �( Ø�AJ?gØ�HJÙ>?�;>á<?�Ù â ;@Ø�à ?�+r�O:\=@CFØ�AJÙ�� �ì$%�:<AJL0� �MêD%R=KÝO:Ê=

& � �N�� � % - �( & � f - �� � �1s� �N � � � & �=N � � � % - �( & � f -*�� � �1U� N � � � �35 & � . �1 �Yê ��6 D �&"% - �&�� �D%A1 � �=�D% � � � �� �KI �D% 3

5 & � . �1 �tê ��6 D & � % -'& � � �D%21 � �Z�D%�� � � �� �@I �D%&�

×�CG=@Ý#:\=1EF?�:<Ù>=|Ø�AJ? Ø â =@ÝJ? CFAM?�+r�O:<EGCG=KCG?�ÙÆH ?ICFAJ�"Ùt=K;>CFßI=�ã ��ÝJCFÙ1Ù>ÝJØ_×�Ù0=KÝO:Ê= ; � � �; :<EFÙ>Ø+CFA�=@ÝJCFÙß�:<Ù>?<ã �VCGAJß�??� �N � �[ � �] %�×�:<Ù|:<;@HMCG=K;@:<;>Ö<ÞJ=KÝJ?6=K;>CFÜJEG??��N � ��[ � �^] � %�CFÙ�CFAJLM?�?�L�=KÝJ?6�JAJC�+}�M?�àË:(&VCFàÈCF��?I;Ø â �� $2"%ã �

���$%�%��k%�� � �$% ��% #"$ #%&� ��VCFAMß�? ��� v ê :<AML �� � � 3«=KÝM? ßIEÑ:<CGà CFA �vC %ËCFÙ"Ø�Heá}CFØ<�JÙ@EhÖÍÙK:Ê=KCFÙtèO?�L â Ø�; $ � � ãÇ� ?=KÝJ?I;@? â Ø�;@?�:<ÜJÜMEGÖ1:\A6CGAJLJ�Jß7=KCGØ�Ag:<;@�<�JàË?IAe=ÏHrÖ0Ù@�JÜJܹØ�Ù>CFAJ��=KÝM?�;@?,?.&MCGÙ>=@Ù $#% �rê��������&�!�X�·ê�"�:\AJL�:ß�Ø�Ae=@CFAr�JØ��JÙ â �JAJß7=KCFØ<A.� ( G = Ú � ( G = �lY F GHG Ù@�MßTÝÉ=KÝO:\= ;8( G = CGÙ�Ø â =KÝJ? â Ø�;@à ;8( G = � f ( G = �

( G == %��& � . f ( G = - �� ( G = 1+�y( G = �Z� ( G == %�� � � ãF<Ð=0×�CFEGE�H¹?ÉÙ@ÝMØd×�A�=@ÝO:\=0=@ÝJCFÙ0CGàËÜMEFCF?IÙ�=KÝJ? â �JAMßI=KCGØ�AO:<E â Ø�;>àËÙØ â ;8($��CGá<?�A�CFA ��C %�:<AML�=KÝM?�Ù@Ø<EF�M=@CFØ�A â �JAJß7=KCGØ�AJÙÆLJ?IèOAM?�L�CGA �vCGC %ãqåa?I=H� ( = %x� ( Þ f ( � � ���(ÈH ?:<;@HMCG=K;@:<;>ÖËHJ�M=�è &V?IL§ã�9DØ<=@CFAJ� â ;@Ø<à �� "%�=KÝO:Ê=0�'�( G = - ���( G = � �1,( ���($CG= â Ø�EGEFØ_×�Ù â ;>Ø�à �Yê �"%q:<AML=KÝJ?gCGAJLJ�Jß7=KCFØ<A�ÝeÖ}ܹØ<=KÝJ?IÙ@CGÙ�=@ÝO:\=�=KÝM?gá\:<EG�J? â �JAJß7=KCGØ�A ;H( Ù@:\=KCGÙ>èO?IÙ;H( � f ( �\� ( = % � àË:(&

; � �E?� � -�� < & �=N � � %_- ( 3 5 � �& � . �1,( � [�- �� ("% -2] � ��1+� ( G = �=� ( = �\�D% �(� � � ( G = �Z�(= �!I �(%

BBB [7� f (�� Ne� ] D 68(7) � ���( C � �eì$%��>

Page 30: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

5Æ=@CFEFCG��CGAJ�'åa?�àÈà3: ! �vÙ>?I=>=KCFAM�U�� � � ( G = �=�(= � i %7Þ �� � �� ( G = Þ �1�� �1 (MÞ,�� � �� ( �1,(VÞ f � f (}Þ

6k� 68(MÞ �( � ( :<AJL � � � ( G = �=� ( = � i %1=@ÝJ?+Ù>Ø�EF�M=@CFØ�A#=KØ�=KÝJ?+àË:(&VCFàÈCF��:\=KCGØ�A�ÜJ;>Ø�HJEF?Ià CFA;� # �"%=T:4�\?�Ù�=KÝJ? â Ø�;>à

N � ( � f (`�\� ( = % � �N4�=� ( = % � f ( - �� ( �] � ( � f ( �\� ( = % � �tê � �N4�=� ( = %B% � f ( - �� ( � &�( �=� ( = %[ �( � f ( �\� ( = % � �tê � �N4�=� ( = %B% � f ( - �� ( � �tê ��6 D( &�( �Z� ( = %)%�� ���(

� #43$%

×�ÝJ?�;>? �N!( �Z� ( = %qÚT� � ê -)� �( �=� ( = % ������ � Y = :<AML� �( �=� ( = % ÚC� �RàË:(&! `b � "� ! $ = < ( 365 & � . �1,( �tê �N6 D( &4% -'&�� �D%A1+�y( G = �Z� ( = �\�D% � � � � ( G = �=�

(= �!I �D% C

&�( �=� ( = % ÚC� :<;@�aàË:(&! `b � "� ! $ = < 3 5 & � . �1,( �tê ��6 D( &"% -'&�� �D%21�� ( G = �=� ( = �\�D%�� � � � ( G = �Z�(= �!I �(%DC �

��ÝJCFÙDÜJ;@Ø_á<?�Ù|=@ÝJ?�Ù>?�ß�Ø<AJL�ß�EF:<CFà ��CFC %�Ø â =KÝJ?·ÜJ;@Ø<Ü Ø�Ù>CG=@CFØ�A§ã=�V�JHJÙt=KCG=@�M=KCGAJ�Ë=@ÝJ?�Ù>Ø�EF�V=KCFØ<AJÙ�CFA � #43$%CFAe=KØ � �eì$%�:<AJL�Ø�àÈCG=>=KCFAM�·=KÝM?·:\;@���JàÈ?�Ae=@Ù � f (��B� ( = % â Ø�;�AJØ\=T:\=@CFØ�AO:\Eyß�Ø<Ará<?�AJCG?�AJßI?���Chá�?IÙ;8( � f ( �\� ( = % � & ��N � ( � � % - ( 3 5 �� �& � . �1,( �K[ �( - ���(A% -�] � ( � � 1�� ( G = �=� ( = �\�D%�� ��� � ( G = �Z�

(= �!I �D%

� & � �N!( �=� ( = % � f ( - �� ("% � � � -�& � �tê�� �N!( �=� ( = %B%�� f ( - ���($%�� � �� ( 365 & � . �1,(8�Yê � 6 D( &�(8�=� ( = %B% -'&�( �Z� ( = %2� �D%21�� ( G = �=� ( = �\�D%�� � � � ( G = �Z�

(= �!I �(%

� & � �N!( �=� ( = % � f ( - �� ("% � � � -�& � �tê�� �N!( �=� ( = %B%�� f ( - ���($%�� � � � �( �Z� ( = %� & � f ( - �� (�� � � � �N!( �=� ( = % � -�� �( �Z� ( = %��tê � �N!( �=� ( = %B% � �� ?Iß�:<EGEFCGAJ��=KÝJ:\= �N ( �Z� ( = %�� � êe-�� �( �Z� ( = % ���� � � Y = =KÝM?6Ù>?�ßIØ�AJL�=@?�;>à5à3:�Ö"H¹?0×�;@Ch=@=@?�A�:<Ù

�N ( �Z� ( = % � -)� �( �=� ( = % �tê � �N ( �Z� ( = %)% � � ê -�� �( �Z� ( = % � �( �=� ( = % ������� êe-�� �( �Z� ( = % ���� � �

� � ê -)� �( �=� ( = % ������ = Y ��V?I=>=KCGAJ� � ( �Z� ( = %ÉÚT� � ê - � �( �=� ( = % ������ � Y = =@ÝJ?�A���CGá<?�Ùg=KÝJ?Èß�EF:<CFà �vC % â Ø�;1=@ÝJ? â �MAJßI=@CFØ�A�;H(Vã?��ÝM?â :<ßI=�=@ÝO:\=�?�:\ßTÝ � ($CFÙ�ßIØ�Ae=KCFAr�JØ<�JÙ�CFÙÆ:<A'CFàÈàË?ILJCÑ:Ê=K?|ßIØ�AJÙ>?�+r�J?�AMß�?ÉØ â ��;@Ø�ܹØ�Ù>CG=KCGØ�A�ê�ã �

����� ��� ����������� � ��������� �� ��VCFAMß�?�=KÝJ?Æß�EF:<CFà CFA*�vC %%CGÙ�:<�e:<CGAËCGàËàÈ?�LJCF:\=K?IEGÖ6ÙK:Ê=KCFÙtèO?�L â Ø�; $ � � ×R?D:<ÜJÜJEhÖÉ=KÝJ?ÆÙK:\àË?ÆCFAJLM�Jß7Û=KCGØ�AÈ:<;@���MàË?IAr=�:\Ù�CGA =KÝJ?�ÜJ;>ØVØ â Ø â ��;@Ø�ܹØ�Ù@Ch=KCGØ�A��gÙ>�JÜJܹØ�Ù@CGAJ�1=KÝJ?I;@?Æ?'&VCFÙt=KÙ $#% �rê����������!�9��ê�"Ù@�JßTÝ«=@ÝO:\=·=KÝJ?Ëß�EÑ:\CFà ��C %1ÝJØ�EFLMÙ â Ø�;�;8( G = ã�åa?I=�� ( = % � ( :\AJL f ( � � ���(�H¹?3:\;@HJCh=K;K:\;>Ö#HJ�M=

�\ì

Page 31: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

è &V?�L§ã�5DÙ@CGAJ��=KÝJ?�;@?Iß��J;>Ù@CGá<?qLJ?7èOAJCh=KCFØ<A��Yê �"%yÖ}CF?�EGLJÙa=KÝJ?,á\:<EF�M? â �MAJßI=@CFØ�A�;H(Æ�JAMLJ?�;Ï=KÝJ?�CFAMLJ�JßI=@CFØ�AÝeÖVܹØ<=@ÝJ?�Ù>CFÙD:<Ù

;8( � f (��B� ( = %�� �;8( � f ( �\� ( = % - ( 3 5 �y( G = �Z�(= �\�D% � ( G = �=�

(= �!I �D% � #VêD%

×�ÝJ?�;>?<Þ�AJØ<=@CFAJ� =@ÝO:\= ( ( ( G = � � ( (�� êD%�:<AJL"=KÝO:Ê=0�'�( G = - ���( G = � �1,( �� ($HeÖ+á}CF;t=K�J?gØ â �� "%�;H( � f ( �\� ( = % ÚC� àË:(&

;�� � � ? � � - � -�� < EFA �=N % - � ( (��ÍêD% 35 �� � EFA � �1,( �K[�- ���($% -�] � �8� � ( G = �Z�

(= �!I �D%

BBB [�� f (�� Ne�X] D 6�(7) � ���( C � � # �4%

5Æ=@CFEFCG��CGAJ�'åa?�àÈà3: ! �vÙ>?I=>=KCFAM�U�� � � ( G = �=�(= � i %7Þ �� � �� ( G = Þ �1�� �1 (MÞ,�� � �� ( �1,(VÞ f � f (}Þ

63��68(VÞ �( � ( (e� ê1:<AML � � �y( G = �Z� ( = � i %k=KÝM?DÙ>Ø�EF�M=@CFØ�A$=KØ6=KÝJ?ÆàË:(&VCFàÈCF��:Ê=KCFØ<A ÜJ;@Ø�HMEF?�à�CGA � # �"%=T:4�\?�Ù�=KÝJ? â Ø�;>à

N � ( � f ( �\� ( = % � �N!( � f ( - ���( �] � ( � f (`�\� ( = % � �Yê � �N ("% � f ( - �� ( � & �([ �( � f (`�\� ( = % � �Yê � �N ("% � f ( - �� ( � �tê���6 D( & �( % � ���(

� # $%

×�ÝJ?�;>? �N!($ÚT� =� � :<AJL

&�( �Z� ( = %�ÚT� :<;>�RàË:(&! � �� 35 �� � EFA � �1 ( �Yê �*& D 68("% -'&�� � � � ( G = �=�

(= �!I �D% BBB & D 6�( ê � �

��ÝJCFÙÆÜJ;>Ødá<?�ÙÆ=KÝJ?6ß�EF:<CFà5CGA ��CFC %7ã �V�JHJÙt=KCh=K�M=@CFAJ�$=KÝJ?6Ù@Ø<EF�M=@CFØ�A0� # "%�CGAe=KØ � # �4%�:\AJL�Ø�àÈCG=>=KCGAJ�É=KÝJ?:<;@�<�JàË?IAe=KÙ�� f ( �\� ( = % â Ø<;�ß�Ø�Aeá�?IAJCF?IAJß�?gÖ}CF?IEFLJÙ

�;8( � f (`�\� ( = % � EGA ��N � ( % - � ( (�� êD% 3 5 EFA � �1,( �K[ �( - ���("% -2] � ( � �8� � ( G = �Z�(= �!I �D%

� EGA ��N � ( % - � ( (�� êD%MEFA � f ( - ���(�� N � ( �- 35 �� �EFA � �1,( �tê � &�(8�=� ( = % D 68(4% -'&�( �Z� ( = %2� � � � ( G = �Z�

(= ��I �D%

� EGA � f ( - �� ( � - � ( (��Íê %MEFA � ( (�� ê�� � ( (%EFA ( ( � # �A%

- 35 �� �EFA � �1,( �tê � &�(8�=� ( = % D 68(4% -'&�( �Z� ( = %2� ��� � ( G = �Z�

(= ��I �D% �

æqØ�àÉHJCGAJCFAM�?� #VêD%,:<AJL � # �A%k��Chá�?IÙ�=@ÝJ?|ßIEÑ:<CGà �vC %7ã ��ÝJ? â :<ß7=R=@ÝO:\=R?�:<ßTÝ �y(6CFÙ,ßIØ�Ae=KCFAr�JØ<�JÙ â Ø�EGEFØ_×�Ù:<�e:<CGA â ;@Ø�à �,;>Ø�ܹØ�Ù@Ch=KCFØ<A�ê�ã �

� ����������� �� � ����������

���������! " #�%$�&#'�(�)+*-,/.10��! # "��0�.KÙ,Ù2�-34��.5�607��'�&#08*- +9���:;&"0��IÙ<.2�+*=.<*-,2��>JÙ?��9@&#'A.5��&GÙ1)�*-)B�6,�C�DE #.2���!>�(!�34�<Ù?.��-�F.5���G,?��Ù2>H #.KÙ�*-,?�gÙ?.7*='�9+*-,?9JIK*A)�,2�;�-�L&FÙ�&"'H0� ">H9���9M���6,2�G���!,��8*<Ù?�G�-�N,?�6���6,2��'H0��-C

O-P

Page 32: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

������������� ��������z�������������! #"��$���&%(')%* ,+.-/�0�213�4�&57698 � � Ú:�<;!= >?����@A�#�B-DCE ����&'��GFHCE571I J%�"I5�-�KML�%N1OL�& #�P��QJ%(57 R��ST ����&'N�P�&576U-��� J%(-VF(+W JL7�91X"�576T%* J%N"�5�-Y8Z� [�]\ � �_^[�`F/"� A�B')'a^cbd�e�&576f�!�HgD^cb��hi8Z�j^[�[k � �_^[�ml&�nk P�oqp Lr�m5 s�t 8Z�j^[�V�u��vE^[�nk s�t � �j^[�V�u��vE^[�&�w4x�yuy:zKÚZ{��!'JÙ?&"9��6,1.2������>H'�06.2&"�!'}|�Ú�~�8�; � $���&"07�4&FÙ 34��*<Ù2>H,5*E�� #��*-'�9}�rÛ &#' .2��(!,2*E�� #�-CZ��� 9��3�MÛ'�&#.2&"�!'�|��j^[�[\ P ���!, *= " &^fb�� *='�9��!�HgD^fb���hi|��_^[�[k P l&�[k P C��n��.2��� 34�!'H�-.5�!'H&"0�& .R� �=�H&#' .2�7Û(!,5*= FÙN�-'����+*\Ù�� t |��_^[���u�JvE^[�n\ P CLD|Ù>Ù2>�3 ���T��$�*D���-�K06�!' .5,2*-9�&"0�.5&#�!'�.5��*=.�� t |��j^[�V�u��v$^[��~ P C�+�! " #�%$�&#'�(`� *=>���,��H�I�$�T� I��H*=.���� O C�� IH)JC�������IH.2��&FÙ�&GÙ��X� >�& :-*= "��' .�.5���u�RgD^�b���hi|��_^[�[k P l&�M~ P I$���&"07� &GÙ * 0��!' .5,2*-9�&#06.5&#�!'JC��E�6'�0��.� t |��_^[���u�JvE^[�}k P *-'H9JI��2� .5��� #&"'���*-,2& .R� �=�E&#' .5��(-,5*- GÙ�I� t 8Z�j^[�V�u��v$^[��k�� t�� �_^[���u�JvE^[� C ����������¡ ��� ¢�£�����¤ H"#�Z"�'�"DST%�1��&'¥-/�0�21X���&576¦�J�����G�J�§� �����¡�������! �"��$���B%)')%/ ,+�-/�0�213�KM%* �L¨�©����%)5�S-DCD���M"� X H�36P"I5] JL7��13"�@��u�21� ª-DC��&-��� `«�¬b9���J�§��­:% o � o ­r�!�B«����~<� o ��� Z®©¯�>�°±�±¬���q�¢13"�@��u�21� -#�I n�B576²|'Ú�®©³��´;7=£>µ���G��1X"�5r J%(5rC�"�CE-§FHCE571I J%N"�5 oqp L7��5�|.%(-���QJ%(5r H��S$ m���&'N�q�&5769 �L7�q@Y�X�¶ Ú�®©;7=£>·6��m¸�57�36P�&- ¶�J¹E�qÚ�~ s t |���¹ ��^[���u�JvE^[�%)-¥13"�5r J%)5rC�"2CE- ow4x�yuy:z�º�» �DÙ?��� $ .5�+* .<.2����,2�X� >�&#,2�634�6' .@ÙG��¼���;½��¾X� �-�0¿ �63434*`�IÀHC,�E&#'���*->���,¥�O�D�$�T� I )JC[� P ���*-,2�gÙ2*=.5&GÙ��+�69JC� *T�a�;&"'�06��� &FÙ�Ù?>�)�) �!,?.2��9 �!' .5���G0��-34)+*=06.�Ù2��..«� I�.2������>�'�0�.5&"�-'.¶ 0�*-'.� � $�,2& .2.2��' *<Ù

¶�J¹E�M~ sZÁt |��J¹ �O^[�V�u��v$^[� ��+�!,A�8*-07�Â��à ��9ĹÂb·® .5���M06�!' .5&"' >��->JÙ 3 *-)H)�&"'�(�|ª��¹ �DÅ��'Ú�«�Æ;7= > &FÙ����!,?�� oÛ 3 �8*<Ù?>�,5*E�H "�*-'�9U�B�->�'�9��69 ��,2�-3 *E� � :!�P�2� .5���M:=*- ">�� «|���¹$��Ú�~ 3 *�Ã7g&|���¹ ��^[�Ih ^Çb «�Gl *-'�9 ��,2�!3È� �� #� $�T�U| �J¹$�"Ú�~ 34&#'7g&|��J¹`��^[��h ^Éb «�¥l CÊ��-.5�@.2�+*=.�� �-.5�Â� �!>�'�9MÙ4*=,2�@$<�� " oÛ 9��#�+'��69�9H>�� .5�.5���0��!3 )+*-0�.5'��IÙ@Ù��-� «� C1���H&FÙ�&"3 )� "&#��Ù1.5�+*=.�.2���G3 *=)9|���¹ �DÅ���&FÙ��rÛ &"' .5�6(!,5*E�H "� ���!,�*- # u¹`b]® C���:�q�n�*<Ù>Ù2>�3 )H.2&"�!'JIB���!, �8*=07�]��ÃH�69�^¦bÂ� .2���A34*-)]|��OÅ ��^[�0Ú!®d;7= > &FÙ 0��!' .5&#' >��!>JÙG*-'H9����'H0�� 0��!' .5&#' >��!>JÙ�*=.��8*=07� ) �!&"' .�¹DË�b]® C� 0D�PÌ�à )� "�-&#.5&#'�( 0��-34)+*=06.5'H��Ù@Ù �-� .5��� Ù2��.�®e³ «�e�T� :;&#,?.5>H� �=� ��� 07�H�!'��EÍaÎ Ù .2�����-,2��3 ��06� C¿ &")JÙ?07�;> .��}�D�$ÀTÏ I+)JCq��Ð��!I+���H���!,?��3Ñ��� CÒ�T��I�.2���G:-*= ">�� «|�Ú�~ 34*BÃrg�hi|���¹ ��^[�IhqÚ7�J¹`��^[�ab½®·³ «�Gl&FÙ $<�� # hÛ 9H�3�+'��69 *='�9�Ù2*=.5&GÙ��+�IÙ`hi|��J¹`��^[��hTÓW«|M���!,�*- " M�J¹ �O^[�nb]®©³ «��C��� >JÙA$��"Ù?���@.5��*=. .5�H�@3 *=)U| ��>� ,�+ " GÙ .2���@,?�X� >�&",?��3 ��' .KÙP� *T��Û�� 0D� &"'��*->���,A�O�I�$�$� I�¿ ��3 3 *�IÀHC,�!I�)JC§� P ����IH$��H&"07� &"3 )� "&#��Ù<.2�+*=.�.2���G3 *-)P¶�HÅÔ��&GÙ�0��!' .5&#' >��!>JÙ6C �

O �

Page 33: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

������������ CD���Z"�-��A �L:�� JL7��@A�#�&-XCE #���6��m¸�57�36�%(5��q-V-DC&@��Z �%�"�5���%)-�-DCX���M"I D H�36¡"�5Ä JLr��@A�#�&-XCE m���&'��-DC��B-#�� «� ~ «�� ³g������³ «�� b·�G� � � o©p L7��5¬�#�21OL¤1X"�5r62%* �%�"�5:�B'¥62%)-X J V%*��C� �%�"�5 ������� ��� �� �DÅ��m­� ~¨� �������5��� %(-a-DCD���Z"� X H�X6P"�5�«� �`KML�%)'N�4 JL7�q@}�& �S$%)5:�&'062%(-D J �%R��C� J%�"I5P� � %)-a-DCX���M"I D H�36."I5�«��� ow4x�yuy:z�º �+�!,��8*=07� 3 �8*\Ù2>�,2*E�� "�6Ù2��.��?b���� � ��$<� �+*8:-��� ~ �����«� ���Â�����U«�� ��$����6,2�!�9���'H�-.5�IÙ .5����>�'�&"�-' �-� 9�&GÙ#"?�!&#' .|Ù?�6.KÙ *-'�9«� &GÙ�.2��� 0��-34)� #��3 ��' .E�-�¥«� CG�;&"'�06��� &FÙÆÙ2>H)�)B�-,?.5�69�!' «$ *-'�9%�&�«�� ¯·«�� $<� �+*8:-���!���'�«�( �M~ P *-'�9M.5���6,2�����!,2�

�u������~¬�u���'��«� �*)Ä�u���'�«� ��~¨�u�+�&�«� � ,-�µb��G� � �&� �JÏ$Ï$�ÊE�-.2&"'�( .5�+* ./.1032 Á4 �5� � �4~6. 0 �5� � �[Å7. Á4 ��� � �G*-'�98. Á4 �5� � ��~:9 �<; � .

Á4>= ���>�T���!'��4�$�H.7*=&"'JÙG.5���

� *-06.2�!,2&(�8*=.2&"�!'��O�$��� *\Ù�u����� ~ �!���&�«� � �/ÏEÀ$�~ s

4s4 ÅIÅIÅ s 4 . 0 �5� � �?.

Á4<@ �5� �A� �5� � �� �mvB� �!ÅIÅIÅC. Á4ED ���<F��G��FB�5� � �mvB�<F��H. Á4�I ��� � �V� � ��vB� � �

~ s Á4�Is Á4ED ÅIÅIÅ s Á4 @ . 0 ��� � �J� ��� � �� �mvB� �!ÅIÅIÅK��FB�5� � �mvB�<F���� � �JvB� � � �

����&FÙ �3�;>�*- "& .R�¡� ��&#'�(.5,2>H�M���-,A*- " L� bW��� � ��,?�X� >�&",?��ÙA.5��*=.A���!,A�8*=07� � ~ � ����������� *-'H9*- " M� �N� �� b � �N� � .5���ËÙ2�6.P«� � 3 >MÙ?.A�+*8:-� ��>� " 3 �8*<Ù?>�,2�=I�& C �-Cd«�����5� ��� �� �B«� �X��~Æ�!C�����'�06� .5���Ù2>�)H)B�!,/.��-� «������� �N� �� �DÅ��13 >MÙ?.�� ��*�Ù?>��JÙ?�6.��-� «� � C������ � *-0�.�.2�+*=. .2���|Ù?>�)�) �!,?.��=��� � &FÙ1.5���|Ù2�6.«��� ���! # "� $�Ù &"3 34�69�& *=.2�� ,����,2�-3 .5����� *-06.1.5�+* .a� � �OÅÔ�M~��PO�Q � �� �OÅ�� &GÙ1&#'�9�>�06��9Y�T� .5���E)�,2�R"?��06.2&"�!'Q � ��06� C )�,?� �-�L�-��¿ ��3 3 *TS2� C �����������.1UV %5W���5YXZ \ P ­ª �L7� 1X"� � #��-*�Z"�576���571X�\[ Ú^]_;�XZ�`_:]7³9>Ma ±�±cb d¨³fe¦³hg�­

[��#ic�5jr�|Ú�~lk��J¾ �nm �Ko7�[bpd¨³feW³%gTqqq ¾) mr)soutvjY~'ic�m}\W;�XZ%w%)-yx/CD���Z�m �Q��&5r6}'N"&K��� �QJLr�m@¢%jQ#z¥1X"�5r J%(5rC�"�CE- ow4x�yuy:z�º½Ê��-.5&#'�(.5�+*=.y[ &|{ 'H�!'v} �634) .R�1}�*-'H9 0��-34)+*=06.G} :=*- ">��69JI�$�� 3 *D� *=)�)� (� .5��� 9��3��'�&~}.5&#�!'J{ (-&#:!�6' &"'��;.5���=�3���µ¿ >�0�*�{��H�I�$��S�I )JC Ï&ÀT��.2�/{2�H�%$ .5��*=.\[ &�{E "� $��6,A} *-'�9>�)H)B�6,A} �H��3 &~}0��!' .2&"' >��!>J{�*=.���*-07� ) �!&#' .4�#iaË��5j�Ëm�ab�� ;�XZ �`_��N³M>La±�± C���~�^�~�J�·¿ �6.4.5��� )B�-&"' .��#iaË��5j�Ëm��b��Ô;�XZ����`_���³M>Ma ±�± � � *-,���&#.2,5*-,O��*-'�9 #�6.��+i�� �5jJ�E����� � �B�*h{?�X� >��6'�0�� .7*�� &"'H(M:=*- #>��>{G&#'��Ô; XZ����`_���³M> a±�± $��H&"07��{2*=.5&|{��+�C{G "&"3T�<���`�+i�� �5jJ�E��~e�+iaË��5j�Ë���C¿ �6.���¾#Ë��nm&Ë��Ko:Ë#���B��*='M*-,V��& .5,2*-,�� ) �!&"' . &#'�[[�+iaË\�5j�Ë���C�» ��{2�H�%$ .5��*=. .5�H��,2� �#à &�{/.n{�*T{2�3� >���'�06��J¾����KmN�`�Ko7�$���N� � $���&"07�%{5*=.2&�{O�+�>{��J¾����KmN�`�Ko7�$�§bf[[�#i��_�5jJ�$�����!,�*- " � *='�9 #&"3��<�����J¾����nm����Go7�T��~�J¾�Ë��nmEË5�Ko:Ë#��C�D\{K{?>�34� �+,G{?.�.5�+* .�iaËqk¬;�XZ *-'�9 9��#�+'��G���!,��8*-07� � \¦�¾`����~ i���) XZ

iaË�) XZ ¾�Ë�� o?� °��� ��~ i���) XZiaË�) XZ

j � °��Ëj � °��� o � °��Ë �^�Ç~©���������&�`� *-'�9hmN�y��~'i���;¾���;co t� jJ�`�

O �

Page 34: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

������' $�� �+*8:!� "&"3 �E���]¾`��~�¾�ËG\ P I+ "&#3T�E���fo � °��� ~'o � °��Ë \ P ���!,��8*=07�f�?~·������������� *-'H9 "&#3T�E����mN�4~ mEË�\W;�XZ Cn��� 0��!' {?.5,?>�06.2&"�!' I:¾`��)smN��)�o t� jJ�4~ i�� ���!,�*- " � *-'�9

m���~&i���; i���) XZiaË�) XZ ��¾#Ë�)pj tË o:Ë#��\8i���; i���) XZ

iaË�) XZ �#iaË�) XZ���~©;�XZ$���&"07�s{?��� $�{ .2�+*=.A&#'�9��6��9¬�J¾����KmN�`�Ko7�2�}b�[[�#i��_�5j �$� ���-,A*- " � C�� ' .5��� {?��06�!'�9�08*�{?�@$�����,?�iaËY~c; XZ �!'H� �$�J{2�6,?:-�>{ ��,2�!3 .5��� 9H�3�+'�& .5&#�!' �-�P[ .2�+*=. .2��� {2��.��A�+iaË���j�Ë�� &|{A*p{2&"'H(! "��.5�!'*-'�9 .5��� )B�!&#' .���¾#Ë��nmEË��Go:Ë���3�>J{?.\{5*=.2&�{/�_�P¾#Ë�~ P IumEËa~·;�XZ *-'�9%o:Ë�~ P C�� ' .5�H&�{�08*�{?�-I 9��3�+'H�¾`��~ P I3m���~�i�� *='�9%o7��~ P ���-,���*-07� � \¦� .5�!{2�6� .2�+*=.��J¾����KmN�`�Ko7�$�§b�[[�+i��<�5jJ�E� ���!,�*- " �*-'�9@ #&"3��<�����J¾�� �KmN� �Ko7�T�M~·� P �D;�XZ � P �M~ �J¾�Ë��nm&Ë��Ko:Ë�� C�����&�{<)�,2� :-�>{�.2�+*=.M[ &|{<&#'�9����69@ C �JC 0-C��-'&#.K{�9��!34*-&"' �-�L9��#�+'�&#.2&"�!' C�p�|�^�~�J� ¿ ��.Ä�+i��`�5jJ�$����� � *='�9µ�J¾����KmN�`�Ko7�$���N� � � � *-,V�H&#.5,2*-,��&{?�X� >���'H0��>{ .7*�� &#'�( :=*- ">��C{ &"'� ;�XZP�8�`_��N³�> a±�± *-'�9&dɳ�e?³ g $���&"07�&{5* .5&�{/�_�¦��¾`� �nmN�`�Ko7�$��b [[�+i��<�5jJ�E�4���!,M*- # � *-'H9 "&#3T�E���`�+i��`�5j �T�G~e�+iaË���j�Ë��4b�� ; XZ�� �`_��N³�> a±�± C`» �!{?��� $ .5��*=.�.5���6,2� �#à &|{?.n{ * 0��!' :-��,2(-��' .{2>�� {2�X� >��6'�0���J¾���� �nmN��� �Go7���D��C� � �-���J¾����nm��`�Ko7�T� �N� � $���&#07��{2*=.5&|{��+�C{ #&"3�����`��¾`���y�KmN�����Ko7���X��~�J¾�Ë��nmEË5�Ko:Ë#��$�����,?�A��¾#Ë��nm&Ë��Ko:Ë��§b�[[�+iaË\�5j�Ë�� CaÊE�=.5� �+,K{/.E.2�+*=.��+i��`�5jJ�$����� � � ��&"'H( * 0��!' :-��,2(-��' .{2�3�;>H��'�06� &#34)� #&"�C{ .2�+*=.A& . 3 >J{/.��B�}�B�!>H'�9���9 C�� ' )+*-,/.5&"06>� *=, .2����,?� �#à &�{/.A:-*= ">��C{ «i \ ;�XZ*-'�9 ) « � °�� k P I��£~e���������&�`� {2>�07� .2�+*=. i��]Ó «i *-'�9 ) « � °�� Ó�j � °��� ���!, *- # � \Ç�!CA� &#'�0���J¾����KmN�`�Ko7�$�9b [��+i�� �5jJ�$�A���-,4*= " � .5��&|{ &#34)H "&"�C{ P ÓѾ`��Ó «i�) XZ IG; XZ Ó mN��Ó «i *-'H9P Ó o � °��� Ó<� «i�) XZ�� � ) « � °�� IJ�Ç~¦���������5�`� C�����'�06�G.2���r{?�X� >���'H0��}�J¾����nm��`�Ko7�T� �N� � &|{��B�->�'�9��69&"3 )� (�;&#'�( .2�����#à &�{/.5�6'�0�� �-�L* 0��!' :-��,2(-��' . {?>��J{?�X� >���'H0��²��¾`� � �nm�� � �Ko7� � ��C� � C�¿ �6.4��¾#Ë��nm&Ë��Ko:Ë#�L��~ "&#3�������J¾���� �nm���� �Ko7���3��C�� .G.5���6,2�����!,2� ,2�63 *-&#'J{ .5� {?��� $ .5�+* .Y��¾#Ë��nmEË��Go:Ë#�4b [��+iaËl��j�Ë���C�� &#'�0��¾`� � \ P I�mN� � \ ;�XZ *-'�9 o7� � \ P I � ~ ������������� ���!, *- # �� \ � �!'�� �+*�{.¾#Ë�\ P ImEËÄ\ ;�XZ *-'�9 o � °��Ë \ P I � ~ ���������5�`� Cµ�+>�,?.2����,?34�-,2�-I\{2&#'�0��Ä�+i�� �5jJ�E� �N� � 0��!' :!�6,2(!�C{.5�.�+iaË��5j�Ë�� IJ{2� 9��;�>{ .2����{2>�� {2�X� >��6'�0��Y�+i�� � �5j � � ���C� � ��06� C�¿ &") {207� >H.����I�EÀTÏ IH) C�ÀTÏE��C������6,2�6���-,2�-I{2&#'�0�� #&"3��n�����+i���� �5jJ���X�M~·�+iaË��5j�Ë��L*-'H9 ���!,L��*-07���A\W� �!'�� ��*�{M¾���� )�mN����)�o t��� jJ����;Ti����§~ P.5��&|{q�;&"�6 "9J{E "&#3������`�J¾�� � )�m�� � )�o t� � jJ� � ;si�� � �a~<¾#Ë�)�mEË�)�o tË j�Ë[;siaËq~ P *='�9 .5�H��,2�����!,2��J¾�Ë��nmEË5�Ko:Ë#�[b%[��+iaËl��j�Ë���C �� ���!�����������

������� �"!$#&%(' �O�I�$�E�T�H�$)+*-,/.103254�67,/*-28:9 *-;=<>6�?A@CBA2D?�C:� )�,?&"'�(!�6,A}:E ��,2 "*-(�I�����,? "&"'M* C ��CF�GIH�J �&#�KL' �O�I�$�$�$�H�NMO* PRQTSU,/.WVX,Y@B:Z-[\*-@]8:03,^?A@`_YBa03[X8:B�C�» *- .5��,�9��Wb�,2>��;.2��,E ��,? *-(HIn�<��,2 #&"'*HC ��C I:�='�9HD >^cK*=(!�-C

FdJ �"�"e G �f#&gh' �O�I�$Ï$Ð$�H�i4j67,/*-28:9lk�[m0 Z-[\*-228n,1Z-Cpo�,?&"'�06�6.5�-'Nq�'�&#:-��,K{?&#.R�Lo�,?�>{K{6CFNr� ste�#IuN'�vxwy'�K�zn�"� J/{ � G ��! �J� P!P ÐE�H�l|m} ' .2���(� 'H��~ 0�&#��'�0#�4�=��oN*D� } D\{A}��1�!>v}�b��doL��' {2&"�-'���B{/.5��3!{ &#'²�;.5�;07�+*�{/.5&#0GÌ�0��!'H�!34&#�>{1$�&#.5�4D {G{2�6.K{ ��I>� &|{206>J{K{?&"�!'�oN*-) ��,§Ï&ÀTÏ IU� ��)+*-,/.53 ��' . �=�Ì�0��-'��!3 &"0>{6I���&#�� "������ #9LqE'�& :!��,G{2& .R�!C

O-O

Page 35: Multi-pERioD CoNsumptioN AND INvEstmENt DEcisioNs uNDER

��H���� z J # � ' �H�I�$�T�$�`�R4j63,/*-28:9���?a?�BA@>k$[A8:9A8n,1Z��I_YBa03[X6 C�o�,2&#'�06.2�!'�qE'�& :!��,G{2& .R�jo�,2�>{G{�I-o ,?&"'�0�.5�!'��Ê�T��*HC ��C=G e G #��D' �O�D�TÐ P �`� |� >� #.2&") ��,2&#� 9�{��!'J{?>�34) .5&"�-'v}C� ' :!�C{?.234�6' .�� �60�&|{2&"�-'J{ ��I��l2�BA[X8:9 *-,�� 9a0��,=0328:9�) B���8:B���I�À P Iu�IÀ O�� ��ÐNS�C

�O�I�$ÐEÀT�H� |� >� .5&#)B�6,2&"�;9¬{��!'J{?>�34) .5&"�-'v}C� ' :!�C{?.234�6' .O� ��0�&|{2&#�!'J{ } DÈ{��!,2,?��0�.5&"�-'p��I�l2�BA[X8:9 *-,�� 9a03,=0328:9�) B���8:B���I�ÀEÀHIrÐ$� O�� Ð$�NS�C

� rG ����� � J �&#���'hv x'�!#" H " Jµ�O�D�TÐ$Ð$�`�%$ *3_1[m?�9a_YBA8n,Y; 8:9a_'& BA8n@`?A@n_YBa03[X8:B�CG� )H,2&"'H(!��,NE �6,2 "*-(�I���6,2 #&"'M*HC ��C� � G ��!�e�� ��" #)(�'+*Xw ' �O�D�$�T�$�`��|/�L�634) �!,5*=,��WbG�6'���,2*- MÌM� >�&" #&)��,?&">�3 �����6�!,��1��I &#'-,�*-,/.'.A0�0�&00/ M *-@n_YBA2�*-@�8:9 *-;1� 9a03,=0328:9a?�I;�69JC��T�32 C;D ,?,2� $��4 C^� ' .5,?&" " #&"( * .5�!,6CTÊE�!,/.5�v}R�E�! # *-'H9�o�>��v} #&�{2�H&"'�(¢{��!3 )+*-'T�-I+D 3!{?.5�6,29+*=3 *HC ��C

� � G ��!�e�� ��" #5(I'6*awy'$v7 x'$K�zn�1! J>{ � G �t! �H�I�TÐNS2�`��|��;.2� 07�+*N{?.5&#0�o�,2�;0��C{K{?�>{G�-� �F��3 �!,5*-,O�ÌM� >�&" #&)��,?& *-�HI98Y03S1[A,/*-;R00/(M *-@n_YBA2�*-@�8:9 *-;:� 9a03,=0328:9a?�I��BCr�NS2Ð � �$Ð$Ð CK G�;�G ����� �R�f#=<L' �O�I�EÀ$�T�H�(|m} )H.2&"34*- "� ' :!�>{/.53 ��' .1*-'�9¢{��-'J{2>�3 )H.2&"�!'�� .5,5* .5��(-&"�>{L>�'�9��6,?>�&�{K�KI*-' qE'H0���,/.7*-&#'P¿ & ���6.2&"3 � *-'�9 � 'J{?>�,5*-'H0�� �HI=VX,Y@BA[X,/*-@]8:03,/*-;#� 9a03,=0328:9�) B���8:B���I!� P I7S�S O�� S$À$ÀHC

K G�;�G ����� �R�f#@<L'�KL' �H�I�TÐ P �H� |m} )H.5&#3 *= � ' :!�C{?.234�6' . *-'H9¡{��-'J{2>�3 )H.2&"�!']� .5,5* .5��(-&"�>{�>H'�9���,>�&�{G�4���!,�*¢{� *�{G{��-� q�.5&# "&#.R���+>�'�0�.5&#�!'J{ �HI#� 9a03,=032�BA@�[X8:9 *-I O � I:ÏE�TÐ � À P Ð C

K�zn�1� J>{ � G �t!i#�w ' �J� P!P ÐE�H� |?���H��>��! "� �-�joF��'J{?&"�!'¤�2�v{/.5�63�{ *='�9 � ��3 �!(!,2*-)���&#0.{��+*-'�(!����!,�D\{K{2��.�o�,2&#0��C{E*='�9�{ *-)H&#.7*= 0�+�!,234*=.5&#�!'p��I^� &�{?0�>J{G{2&"�-'NoL*-)B�6,GÏ&À P I>� ��)�*-,?.234�6' .��-��Ì�0��N}'��-34&#0>{�I���&"�6 "�6���6 "9Lq�'�&#:-��,K{?&#.R�-C

K�zn�1� J>{ � G �t!i#lwy' v (I'@ J ��A J � {=H �#B J � �J� P!P ÀT�`�W| }�' .5�H� �¥�;'+*-3 &"0C{��-��D {G{2��.o�,2&#0��>{*-'H9�oL�-,?.2���- "&"��{J&"' *C >� #.2&") ��,2&#� 9�{�Dlo� ��I#D _^*10�?FE=<I03; 8n@C03,^?�*-,/.HGI[\*19A@:*-; ?�IE�&��� O � I$ÏEÐE� � ÏE�NS�C

I ��B J �J�3� �"�/#J(�':��' �H�I�$�TÐ$�`�K�I_YBa03[A6�00/�Gf8n,/*-,=9A8]*-;14�Ba9A8 ?A8:03,MO*�&38n,1Z-CL>��%$�34*-'��´¿ &#.2.2 "�#�+�� #9JI�F�-.5� $�*9��Ê�T� C

%�zNM1��OIs H "JAY#�!R' �O�D�$ÀTÏ$�`�QP(BA,=BA[ *-;R� 0FSY03; 0 Z-6 C�� 07�+*=>�3 o�>��� "&|{2��&#'�(¢{��!3 )+*-'T�!C��s J �TM1�"#U�D'V!R' �O�I�EÀTÏ$�H� |?����� DE0�0�>H3 >� * .5&"�-' �-�W>�&|{K�T�¤{ *-)H&#.7*= 5� Dc� �X� >��6' .2& *- �q�.5&# "& .R�DE'+*- (�B{?&�{ �HI#� 9a03,=032�BA@�[X8:9 *-I O!P �+S2� I:Ð$�E� � ÐNS O C

���"zN� ; G #V!R' �O�I�E�TÐ$�H� VX,Y@�[m0 .-SY9A@�8:03, @0OMO*-@`_YBA2�*-@]8:9 *-;RGf8n,/*-,=9aB�CZ�� *-0�� $<�� # o >��� "&|{2���6,K{�� '�0-I *N{K{5*=07�;> {2�6.?.n{6C

gd� e J �&# � ' �H�I�$�$À$�H�X� .Y�3*-,=9aB .�MO*19A[a0�Ba9a03,=0328:9a?�CZ 0�b�,5*8$ � ��&" # I�Ê��6$ �1�!,K�KC!#"�� ; JZ[ #5<L' %l' v gh'\��' % H O G � �O�I�E��S2�H��) Ba9AS1[m?A8N�-B�M�BA@`_Y0 .3?�8n,-� 9a03,=0328:9d4j67,/*-28:9a?^]�E*-,?:=*-,?9 q�'�&#:-��,G{2&#.R� o�,?�>{K{6I7{ *-3���,?&"9�(!�=C

O S