La remise en cause du modele classique de la finance par

Benoıt Mandelbrot et la necessite d’integrer les lois de

puissance dans la comprehension des phenomenes

economiques

Philippe Herlin

To cite this version:

Philippe Herlin. La remise en cause du modele classique de la finance par Benoıt Mandelbrot etla necessite d’integrer les lois de puissance dans la comprehension des phenomenes economiques.Economies et finances. Conservatoire national des arts et metiers - CNAM, 2012. Francais. .

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https://tel.archives-ouvertes.fr/tel-00787464

Submitted on 12 Feb 2013

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1

ÉCOLE DOCTORALE Abbé Grégoire – ED 546

ÉQUIPE de RECHERCHE : LIRSA EA 4603

THÈSE

présentée par :

Philippe HERLIN

soutenue le : 19 décembre 2012

pour obtenir le grade de : Docteur du Conservatoire National des Arts et Métiers

Discipline/ Spécialité : Sciences de gestion / DOC 07 – Expertise et Ingénierie Financière

La remise en cause du modèle classique de la finance

par Benoît Mandelbrot et la nécessité d’intégrer les lois

de puissance dans la compréhension des phénomènes

économiques

Thèse sur travaux :

Ouvrage principal : Repenser l’économie (Eyrolles 2012), ainsi que :

- Théorie des marchés financiers : revenir aux concepts fondamentaux (Club Finance HEC,

étude n° 75, octobre 2008)

- Finance : le nouveau paradigme (Eyrolles, 2010)

- France, la faillite ? (Eyrolles, 2010, 2012)

- L’or, un placement d’avenir (Eyrolles, 2012)

THÈSE dirigée par :

M. DUBOIS Denis Professeur des universités, CNAM

RAPPORTEURS : M. MAROIS Bernard Professeur HEC, Président du Club Finance HEC

M. MOULIER BOUTANG Yann Professeur des universités - Université de technologie de Compiè-

gne

JURY : M. BÉRA Michel, Président Professeur, CNAM, Titulaire de la chaire de modélisation statistique

du risque

M. ZALILA Zyed Professeur associé, Université de technologie de Compiègne, Pré-

sident Société Intellitech M. MARCOMBES Eric Président, société COGITAM

M. LORENZI Jean-Hervé, excusé Professeur des universités, Paris Dauphine, Président du Cercle

des économistes

2

Résumé

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Mots clés

2*0&"(@3%68#U*("@8#2*34%5,678#9:*3;"8#<(*)48#9):%("+8#=*$*8#!%,#0%3$*("8# (%,#&"#;.,++*0)"8#N*3"6%8# Y*T"48# ?)%("# *.63,):,"00"8# 3?+"*.8# 3?/("L,Q,6?8# $%00*,"# )%$;(?$"06*,3"8# +T+6'$"#$%0?6*,3"#&,Q"3+,/,?#

3

Résumé en anglais

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

Mots clés en anglais

2*0&"(@3%68#U*("@8#2*34%5,678#9:*3;"8#<(*)48#9):%("+8#=*$*8#0%3$*(#(*58#;%5"3#(*58#N*3"6%8#Y*T"48#[.+63,*0#9):%%(8#0"65%348#3"/("L,Q,6T8#)%$;("$"06*3T#).33"0)T8#&,Q"3+,/,"&#$%0"6*3T#+T+6"$#

4

Table des matières

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#b>#!"+#$%&'("+#)%06,0."06#&KM63"#.6,(,+?+#"6#3*/,+6%(?+c# # # # # Bd#

#]>#!K"063";3,+"#)%06*$,0?"#;*3#(*#/,0*0)"#P*.++,"00"# # # # # DB##e>#N%.3-.%,#("+#(%,+#&"#;.,++*0)"#a#!*#0%6,%0#&K"063%;,"# # # # # Db##d>#!*#3"$,+"#"0#)*.+"#&"#(*#Q*(".3#/%0&*$"06*("# # # # # # De##C>#N%.3-.%,#&"+#@.(("+#a#!*#0%6,%0#&"#3?/("L,Q,6?# # # # # # `G##BG>#U:?%3,"#&"#(*#;3%;%36,%0#&,*P%0*("# # # # # # # ``##BB>#!"#)3,6'3"#+)*(*@("_0%0F+)*(*@("8#.0"#0%.Q"(("#6:?%3,"#&.#;%36"/".,(("# # `e##BD>#W%0+,&?3"3#(K?)%0%$,"#)%$$"#.0#3?+"*.## # # # # # EG##B`>#f0"#*;;(,)*6,%0#&.#$%&"#&"#;"0+"3#g#"0#3?+"*.#h#\#("+#$%00*,"+#)%$;(?$"06*,3"+#ED##BE>#!"#)*+#&"#(K%3# # # # # # # # # # EE##Bb>#!*#)3,+"#&"#(*#7%0"#".3%# # # # # # # # # Ee##B]>#f0#;".#&K:,+6%,3"#\#(*#;(.+#P3*0&"#)3,+"#/,0*0),'3"#&"#6%.+#("+#6"$;+## # # EC##W%0)(.+,%0#\#-."(("#+.,6"#a# # # # # # # # # bB##<,@(,%P3*;:,"# # # # # # # # # # # b`##

5

Introduction

6

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7

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b#M&J#$").%$&'(&7#'1"1.*.)@8#2*)$,((*08#BCDBH#

6 Olivier Favereau « L'incertain dans la "révolution keynésienne" : l'hypothèse Wittgenstein »,

Economie et sociétés tome XIX n°3 mars 1985

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15

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16

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16 Claude Shannon, Warren Weaver, Théorie mathématique de la communication, Retz ,1949.

26

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27

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28

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50

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51

Conclusion

52

T%"(,'/)%"*+*0'1,,1*/')#1*H*

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53

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54

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- Markowitz Harry, Portfolio selection, Journal of Finance 1952

F#2":3*#n*S0,+:8#N3"+)%66#V&5*3&8#g#J>$&=/0.)@&7#$-.0-&.(&!$)#'%3$)&W8&hU=!#CbDb8#DGG`#F#2"0&'+F=3*0)"#2,):"(8##g#j,$"0+,%0#"6#"063%;,"#&"+#)%.3@"+#3?P.(,'3"+#h#,0#\.-$(%.'(&('(&$().C#$%&$)&"33*.,").'(%#+%.+#(*#&,3")6,%0#&"#^H#W:"3@,68#2*++%0#BCde#"6#g#j,$"0+,%0#"6#"0F63%;,"#h#,0#D$%&)>+'#.$%&4$&*"&,'-3*$H.)+8#9".,(#BCCB#- Merton Robert, « On the Pricing of Corporate Debt: the Risk Structure of Interest Rate », Journal of Finance 29, 1974

F#y3(?*0#[0&3?8#g#!*#0%6,%0#&"#Q*(".3#/%0&*$"06*("#"+6F"(("#,0&,+;"0+*@("#J#(*#6:?%3,"#/,0*0F),'3"#a#h#,0#!$:"#4%&,#'.%+%&%0#&*B+,'('-.$8#0�#`8#$*3+#DGGd8#!*#j?)%.Q"36"#F#N"6"3+#V&P*38#G>"'%&"(4&'#4$#&.(&,"3.)"*&-"#Q$)8#i%:0#Z,("T8#BCCG#- Pierrat Christian, La gestion financière de l’entreprise, La Découverte, coll. Repères, 2006

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F#n*+:"Q+4T#O,)%(*+8#N")>$-").,"*&1.'*':@&';&%',."*&1$>"2.'#8#W:,)*P%8#U:"#.0,Q"3+,6T#%/#W:,F)*P%#;3"++8#BCbB#F#9*($%0#="(,L8#g#!$,.3$&;'#&4.%"%)$#K&)>$&;'#-0*"&)>")&Q.**$4&^"**&V)#$$)&W8#^.#$48#D`#/?Q3,"3#DGGCH#F#9):%.6"0+#Z,$8#D+2@&3#',$%%$%&.(&E.("(,$8#i%:0#Z,("T#�#9%0+8#DGGDH#F#9"3Q*(#i"*0F=3*0X%,+8#U3*0,?#i"*0FN*+)*(8#D"&N'((".$&2.#)0$**$8#VT3%(("+8#DGBB#F#9".3%6#=3*0X%,+8#g#!"+#)3,+"+#@*0)*,3"+#"0#I6*(,"#*.#2%T"0F[P"#\#.0#"++*,#&K*;;(,)*6,%0#&"#(*#6:?%3,"#&"#2,0+4TF�,0&("@"3P"3#h8#i%.30*(#&"+#?)%0%$,+6"+8#&?)"$@3"#DGGD#F#9:*00%0#W(*.&"8#Z"*Q"3#Z*33"08#J>+'#.$&-")>+-")./0$&4$&*"&,'--0(.,").'(8#n"67#8BCEC#F# 9%30"66"# j,&,"38&g#j3*P%0F�,0P8# <(*)4# 95*0+# *0&# 6:"# ;3"&,)6,%0# %/# )3,+"+#h8# i()$#(").'("*&X'0#("*&';&J$##"%3",$&V,.$(,$&"(4&=(:.($$#.(:8#S.,(("6#DGGC#F#9%3%+#^"%3P"8#_0$*/0$%&*$b'(%&).#+$%&4$&*"&,#.%$8#j"0%l(8#DGBG#- Taleb Nassim, Force et fragilité, Les Belles Lettres, 2010

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F#�*S&"05"@"3#j*0,"(8#j,'('-.$&4$%&$H)#`-$%8#W:*$;+#=(*$$*3,%08#DGGB8#?&,6,%0#3"Q."#"6#*.P$"06?"#"0#DGGC#

55

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naire

Résumé

Le modèle classique de la finance (Markowitz, Sharpe, Black, Scholes, Fama) a, dès le début, été remis en cau-

se par le mathématicien Benoît Mandelbrot (1924-2010). Il démontre que la loi normale ne correspond pas à la

réalité des marchés, parce qu’elle sous-estime les risques extrêmes. Il faut au contraire utiliser les lois de puis-

sance, comme la loi de Pareto. Nous montrons ici toutes les implications de ce changement fondamental sur la

finance, mais aussi, ce qui est nouveau, en ce qui concerne la gestion des entreprises (à travers le calcul du coût

des capitaux propres). Nous tentons de mettre à jour les raisons profondes de l’existence des lois de puissance

en économie à travers la notion d’entropie. Nous présentons de nouveaux outils théoriques pour comprendre la

formation des prix (la théorie de la proportion diagonale), des bulles (la notion de réflexivité), des crises (la

notion de réseau), en apportant une réponse globale à la crise actuelle (un système monétaire diversifié). Toutes

ces voies sont très peu, ou pas du tout exploitées. Elles sont surtout, pour la première fois, mises en cohérence

autour de la notion de loi de puissance. C’est donc une nouvelle façon de comprendre les phénomènes écono-

miques que nous présentons ici.

Mandelbrot, Taleb, Markowitz, Sharpe, Black, Scholes, Fama, Loi normale, loi de puissance, Pareto, Hayek,

école autrichienne, réseau, réflexivité, monnaie complémentaire, système monétaire diversifié

Résumé en anglais

The classical model of finance (Markowitz, Sharpe, Black, Scholes, Fama) has, from the beginning, been chal-

lenged by the mathematician Benoit Mandelbrot (1924-2010). It shows that the normal distribution does not

match the reality of the market, because it underestimates the extreme risks. Instead, we must use the power

laws, such as the Pareto law. We show the implications of this fundamental change in the finance, but also in

the management of companies (through the calculation of cost of capital). We try to update the underlying rea-

sons for the existence of power laws in economics through the concept of entropy. We present new theoretical

tools to understand price formation (the theory of diagonal proportion), bubbles (the notion of reflexivity), cri-

sis (network concept), providing a comprehensive response to the current crisis (a diversified monetary sys-

tem). All these ways are very little or not at all exploited. They are mostly for the first time, made consistent

around the notion of power law. This is a new way of understanding economic phenomena presented here.

Mandelbrot, Taleb, Markowitz, Sharpe, Black, Scholes, Fama, normal law, power law, Pareto, Hayek, Austrian

School, network, reflexivity, complementary currency, diversified monetary system