suibe (shanghai university of international business and economics)
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SUIBE (Shanghai University of International Business and Economics)
Authors introduction
ZHAO Lei
GAO Jianli
Associate ProfessorDepartment of Risk and InsuranceSchool of Financial managementShanghai University of International Business and Economics Email: zhaoleiswm@163.comMembership: GARP (Global Association of Risk Professionals) PRMIA (Professional Risk Manger International Association) APRIA (Asia Pacific Risk And Insurance Association )
Academic Master CandidateSchool of Financial management Shanghai University of International Business and Economics Email: jianligao110@gmail.com Membership: GARP (Global Association of Risk Professionals) HKAFE (Hong Kong Association of Financial Engineer) TAFE (Taiwan Association of Financial Engineer) SESC (Systems Engineering Society of China)
Research area: household finance decision-making, household risk management
1.Introduction 2.Model setup 3.Simulation 4.Conclusion
1.1 Research Background:
Mid-1930s
Now
Development of national/regional economy
Improvement of public welfare
Perfection of household risk management
Innovation of household finance
Research emphasis Research types
Normative research(Domestic references:12)(Foreign references:15)
Decision-making mechanism of household
Consumption/saving
Influencing factors of household consumption/saving
Empirical research(Domestic references:6)(Foreign references:11)
Research aim
1.2 Review: Household decision
Consumption Saving
Absolute income& Relative income hypothesis
Absolute income& Relative income hypothesis
LI-PIHLI-PIH
Random migration hypothesisRandom migration hypothesis
CEQCEQ
C=c(Y),S=s(Y),0<c<1,c+s=1
C=c(Y),S=s(Y),0<c<1,c+s=1
Life-cycle motiveLife-cycle motive
LILI
PIPI
IntertemporalIntertemporal
Quadratic utility functionQuadratic utility function
Bequest motiveBequest motive
UncertaintyUncertainty
Precautionary saving theoryPrecautionary saving theory
1)Life-Cycle motive1)Life-Cycle motive
2)Intertemporal substitution2)Intertemporal substitution
3)Precautionary motive3)Precautionary motive
4)Bequest motive4)Bequest motive
5)Improvement motive5)Improvement motive
6)Independent motive6)Independent motive
7)Enterprise motive7)Enterprise motive
8)Avarice motive8)Avarice motive
9)Downpayment motive9)Downpayment motive
1)Life-Cycle motive1)Life-Cycle motive
2)Precautionary motive 2)Precautionary motive
3)Other motives3)Other motives
1) Risk aversion utility function2) Inter-temporal decision
3) Uncertainty of future income4) Life-cycle
5) Optimization
1) Risk aversion utility function2) Inter-temporal decision
3) Uncertainty of future income4) Life-cycle
5) Optimization
1) Risk aversion utility function1) Risk aversion utility function 2) Inter-temporal decision2) Inter-temporal decision
5)Uncertainty of future income5)Uncertainty of future income4) Life-cycle4) Life-cycle3) Optimization3) Optimization
1 1
1 1
1 1
11 1
21 1 1
~max ( ) [ ( ) ( )]
= max [ ] [ ( )( )]
~. . ( )
, ~ (0, )
T
Ct
Ct
sj
st t js t j t
sTC Cjt st js t j t
tt t t t
t t t t
U C E U C
e E e
s t W R W C Y
Y Y
1.Introduction 2.Model setup 3.Simulation 4.Conclusion
1.2 Problem:
a) Normative research
b) Empirical research
Only income uncertainty
Negative exponential utility function
Difficulty of life-cycle characteristics
Imperfect panel data
Arguable dummy variable
Accidental expenditure: personal risk, property risk, liability riskPower utility function with wealth accumulation motive
Set decision-making characteristic based on life-cycle model
1.3 Improvement:
Simulation: generate income series based on real environment
Complicated combinatorial optimization
3-D ACA (3-Dimension Ant Colony Algorithm)
Simulation: accidental expenditure in triangular distribution
Know of global information of income Visible range assumption
1.Introduction 2.Model setup 3.Simulation 4.Conclusion
2.1 Risk aversion function:
Risk aversion utility function
Form of utility function
Monotonousness & Concavity
Measurement of risk aversion
ARA RRA
Concave quadratic utility function
U(c)=c-(a/2)*c2 U(1)(c)>0;U(2)(c)<0; a/(1-a*c) a*c/(1-a*c)
Negative exponential utility function
U(c)=-(1/θ)*e– θ*c U(1)(c)>0;U(2)(c)<0; θ θ*c
Power utility function U(c)=c1-ρ/(1-ρ) U(1)(c)>0;U(2)(c)<0; ρ/c ρ
Hyperbolic absolute risk aversion utilityfunction
U(c)=(1/r-1)*(a*c/(1-r)+b)r U(1)(c)>0;U(2)(c)<0; (c/(1+r)+b/a)-1 (1/(1+r)+b/(a*c))-1
CARA (Constant Absolute Risk Aversion)CRRA (Constant Relative Risk Aversion)
''(c)=
'(c)
UARA
U
''(c)=
'(c)
UARA c
U
tt t t-1 t t-1 1 0 1 1 2 1 3 t 4
c
1W(a , y ,c ) = Max - exp[-θ((c - λc ) + η(a - a ))] [ exp( a c )]
θ t t t t tE y
t t-1 1 0 1 3 1 1 2 1 3 t 4(1- η)exp[-θ((c - λc ) + η(a - a ))] = [ ( )exp( a c )]t t t t tE y 2
12 1 2 1 122
1[exp( )] exp( ) exp(- )d
22t
t t t tE
LEI Qinli (2009)
Keys of successful solution:
a) Exponential function
b) Guassian distribution of uncertainty
11 1
1 1
[(c c ) (w w )](c c , w w )
1t t t t
t t t tU
CRRACRRA
Consuming habitConsuming habit Wealth accumulation motiveWealth accumulation motive
1.Introduction 2.Model setup 3.Simulation 4.Conclusion
1.Introduction 2.Model setup 3.Simulation 4.Conclusion
2.2 Inter-temporal model
Time preferences:
Income fluctuation:
Accidental expenditure:
1, t;( )
, .td
t
~
1 1
~ ~
(t)
(t) s(t) (t)
t t ty g y
g w
~ ~ ~ ~
1 2 3t t t te e e e
Set β,δ based on life-cycle characteristics
Generate s(t) randomly in Gaussian distribution based on Shanghai social average wage growth rate (1994-2012)
Set w(t) based on different setup of career characteristics
α,γ are weighting coefficient
Personal, property, liability accidental expenditure
Following different triangular distribution
t t-1
τ-tt t-1 t t-1 t t t-1 t t-1
c ,cτ=t+1
Max U(c - λc , w - w ) + E βδ U(c - λc , w - w )T
t t-1
1-ρ 1-ρτ-tt t-1 t t-1 τ τ-1 τ τ-1
tc ,c
τ=t+1
[(c - λc ) + η(w - w )] [(c - λc ) + η(w - w )]= Max + E βδ
1-ρ 1-ρ
T
~s.t. w = (1+ r (τ))w + y - cτ τ τ ττ+1 e
Optimization
1.Introduction 2.Model setup 3.Simulations 4.Conclusion
2.3 Household life-cycle model:
Stages:
Age:
Child:
Age:
Stages:
25 27 30 36 42 48 52 55 60 75
0 6 12 18 22 25
YoungSingle
Cohabitingcouples
Middle-agedcouples
Old-aged couplesin retirement
Preschool Elementaryschool
Junior-senior high school
College Transition to independence
Table b. Characteristics of household life-cycleTable b. Characteristics of household life-cycle Set change law of β , δ , η , ρ
3.1 ACA (Ant Colony Algorithm)
t t-1
1-ρ 1-ρτ-tt t-1 t t-1 τ τ-1 τ τ-1
tc ,c
τ=t+1
[(c - λc ) + η(w - w )] [(c - λc ) + η(w - w )]Max + E βδ
1-ρ 1-ρ
T
~s.t. w = (1+ r (τ))w + y - cτ τ τ ττ+1 e
~ ~ ~ ~
1 2 3t t t te e e e
~
1 1
~ ~
(t)
(t) s(t) (t)
t t ty g y
g w
complicated combinatorial optimization
3-dimensional path planning algorithm of ant colony algorithmM. Dorigo(1997)
Transportation engineering
Electricity engineering
Communication engineering
Chemistry engineering
be used in solving optimization problem
1.Introduction 2.Model setup 3.Simulation 4.Conclusion
3.1 ACA (Ant Colony Algorithm)
Modeling of 3-dimensional environmentModeling of 3-dimensional environment
Start of searching pathsStart of searching paths
Searching nodesSearching nodes
Whether it’s the end or notWhether it’s
the end or not
Updating pheromoneUpdating pheromone
Whether algorithm is finished or not
Whether algorithm is finished or not
Getting the optimal 3-dimensional pathGetting the optimal 3-dimensional path
Y
Y
N
N
T
CS
∏i
k+1k
j+1j
C
S
yi = ci + si
Lx,max= one year
5 1015 20 25
30 35 40 4550
1020
3040
5060
70
20
40
60
80
100
120
140
Age
Decision information space
Consumption
Sav
ing
1.Introduction 2.Model setup 3.Simulation 4.Conclusion
3.2 Simulation scheme setup
Parameters Personal accidental expenditure
Property accidental expenditure
Liability accidental expenditure
Total accidental expendture
(a1,b1,c1) (0.005,0.5,0.001) (0.007,0.2,0.003) (0.001,0.1,0) (0.013,0.8,0.004)
(a2,b2,c2) (0.007,0.5,0.003) (0.009,0.2,0.005) (0.003,0.1,0.002) (0.019,0.7,0.010)
(a3,b3,c3) (0.005,0.55,0.001) (0.007,0.25,0.003) (0.001,0.15,0) (0.013,0.95,0.004)
1.Without accidental expenditure
2.With accidental expenditure
a: minimum coefficientb: maximum coefficientc: mean coefficient
0 2 4 6 8 10 12 14 16
x 104
0
5
10
15
20
25
30
35
Personal accidental expenditure
Fre
quen
cy(f
or 1
500
times
)
Triangular distribution of personal accidental expenditure in simulation 1
0 1 2 3 4 5 6 7
x 104
0
5
10
15
20
25
30
35
Property accidental expenditure
Fre
quen
cy(f
or 1
500
times
)
Triangular distribution of property accidental expenditure in simulation 1
0 0.5 1 1.5 2 2.5 3 3.5
x 104
0
5
10
15
20
25
30
35
Liability accidental expenditure
Fre
quen
cy(f
or 1
500
times
)
Triangular distribution of liability accidental expenditure in simulation 1
0 2 4 6 8 10 12 14 16
x 104
0
5
10
15
20
25
30
Personal accidental expenditure
Fre
quen
cy(f
or 1
500
times
)
Triangular distribution of personal accidental expenditure in simulation 2
0 1 2 3 4 5 6 7
x 104
0
5
10
15
20
25
30
35
40
Property accidental expenditure
Fre
quen
cy(f
or 1
500
times
)
Triangular distribution of property accidental expenditure in simulation 2
0 0.5 1 1.5 2 2.5 3 3.5
x 104
0
5
10
15
20
25
30
35
Liability accidental expenditure
Fre
quen
cy(f
or 1
500
times
)
Triangular distribution of liability accidental expenditure in simulation 2
0 2 4 6 8 10 12 14 16 18
x 104
0
5
10
15
20
25
30
35
Personal accidental expenditure
Fre
quen
cy(f
or 1
500
times
)
Triangular distribution of personal accidental expenditure in simulation 3
0 1 2 3 4 5 6 7 8
x 104
0
5
10
15
20
25
30
35
Property accidental expenditure
Fre
quen
cy(f
or 1
500
times
)
Triangular distribution of property accidental expenditure in simulation 3
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 104
0
5
10
15
20
25
30
35
Liability accidental expenditure
Fre
quen
cy(f
or 1
500
times
)
Triangular distribution of liability accidental expenditure in simulation 3
1.Introduction 2.Model setup 3.Simulation 4.Conclusion
3.3 Results:
5 10 15 20 25 30 35 40 45 50
10
20
30
40
50
60
70
50
100
150
T
Age: (A+24) years old
Optimal path without accidental expenditure
S
Consumption: (C) 10,000 Yuan
Savi
ng: (
S-72
) 10,
000
Yuan
Optimal path of household consumption and saving inter-temporal uncertainty decision in life-cycle without accidental expenditure
1.Introduction 2.Model setup 3.Simulation 4.Conclusion
3.3 Results:
Optimal paths of household consumption and saving inter-temporal uncertainty decision in life-cycle with accidental expenditure
5 10 15 20 25 30 35 40 45 50
10
20
30
40
50
60
70
50
100
150
T
Age: (A+24) years old
Optimal path with accidental expenditure in simulation 1
S
Consumption: (C) 10,000 Yuan
Sa
vin
g: (
S-8
8) 1
0,0
00
Yu
an
5 10 15 20 25 30 35 40 45 50
10
20
30
40
50
60
70
50
100
150
T
Age: (A+24) years old
Optimal path with accidental expenditure in simulation 2
S
Consumption: (C) 10,000 Yuan
Sav
ing:
(S-8
8)10
,000
Yua
n
5 10 15 20 25 30 35 40 45 50
10
20
30
40
50
60
70
50
100
150
T
Age: (A+24) years old
Optimal path with accidental expenditure in simulation 3
S
Consumption: (C) 10,000 Yuan
Sav
ing:
(S-8
7) 1
0,00
0 Y
uan
Simulation1 Simulation2
Simulation3
Simulation 0Simulation 1Simulation 2Simulation 3
Comparison
1.Introduction 2.Model setup 3.Simulation 4.Conclusion
3.3 Results:
Collection of points: lower than moving average consumption for 5years
τ=t-4
1
5
t
tc c
1.Introduction 2.Model setup 3.Simulation 4.Conclusion
3.3 Results:
Items(of optimal
consumption growth rate)
Without accidental expenditure
With accidental expenditure 1
With accidental expenditure 2
With accidental expendture 3
Mean 0.0335 0.0341 0.0361 0.0333
Standard deviation 0.1183 0.1282 0.1469 0.1209
VaR -0.1000 at 10% -0.1025 at 14.00% -0.1034 at 20.00 % -0.1 at 12.00%
[1] For example, -0.1000 at 10% means the probability of that the growth rate of household optimal consumption is lower than -0.1000.
Increase minimum & mean
Increase maximum
1.Introduction 2.Model setup 3.Simulation 4.Conclusion
CRRA utility
Consuminghabit
Wealth accumulation
motive
Life-cycle
Household optimal decision
Consuminghabit
Timepreferences
Incomeuncertainty
Accidentalexpenditureuncertainty
4.1 Successful solutions:
Get the optimal path through 3-d ACA
4.2 Find:
1) accidental expenditure increases the VaR of consumption negative growth rate2) household consumption inter-temporal uncertainty decision is more sensitive to the perceived
minimum and mean than the perceived maximum of accidental expenditure
1.Introduction 2.Model setup 3.Simulation 4.Conclusion
New progress
Styles of household
Growing income Stabilized income Fluctuant income
ρ 0.99(a) 0.55(b) 0.99(a) 0.55(b) 0.99(a) 0.55(b)
η 0.05(c) 0.01(d) 0.05(c) 0.01(d) 0.05(c) 0.01(d) 0.05(c) 0.01(d) 0.05(c) 0.01(d) 0.05(c) 0.01(d)
New progress
510
15
2025
3035
40
4550
5
10
15
20
25
30
35
40
45
50
20
40
60
80
100
TTTT
Age: (x+24) years old
SSSS
Consumption: y*10,000 Yuan
Sav
ing:
(z-4
1)*1
0,00
0 Y
uan
data1 data2 data3 ac data5 data6 data7 ad data9 data10 data11 bc data13 data14 data15 bd
10
20
30
40
50
60
70
80
90
New progress
510
1520
25
3035
40
4550
2
4
6
8
10
12
14
16
18
20
22
10
20
30
TTTT
Age: (x+24)years old
SSSS
Consumption : y*10,000 Yuan
Savi
ng: (
z-11
)10,
000
Yua
n
5
10
15
20
25
30
data1 data2 data3 ac data5 data6 data7 ad data9 data10 data11 bc data13 data14 data15 bd
New progress
5
10
15
20
25
30
35
40
45
50
5
10
15
20
25
30
35
40
45
20
40
60
80
TTTT
Age: (x+24)years old
SSSS
Consumption: y*10,000 Yuan
Savi
ng: (
z-36
)*10,
000
Yuan
10
20
30
40
50
60
70
80
data1 data2 data3 ac data5 data6 data7 ad data9 data10 data11 bc data13 data14 data15 bd
New progress
Styles of income Growing income Stabilized income Fluctuant income
Styles of decision ac ad bc bd ac ad bc bd ac ad bc bd
Mean of consumption(10,000 Yuan)
27.921 28.490 27.254 28.862 14.294 15.568 15.098 15.235 20.882 25.803 28.156 22.960
Standard deviation of consumption(10,000 Yuan)
7.657 7.262 6.764 7.502 3.500 3.695 3.722 3.766 4.902 6.020 7.393 7.626
SD/ME 0.274 0.255 0.248 0.260 0.245 0.237 0.246 0.247 0.235 0.233 0.263 0.332
VaR of negative saving (-0.4 of
average incmoe)
17.65% 13.73% 11.76% 29.41% 1.96% 3.92% 0.00% 0.00% 35.29% 35.29% 39.21% 19.61%
SUIBE (Shanghai University of International Business and Economics)
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