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)