巨灾保险博弈分析

摘要：近年来，中国经历了许多巨灾。虽然今年年底将推出巨灾保险，中国在此领域还需进一步探索。旨在用博弈论的知识分析即将推行的巨灾保险机制的不足之处，并提出合理性的建议。

关键词：巨灾保险；博弈分析；保险机制

中图分类号：F84文献标志码：A文章编号：1673-291X（2011）03-0066-02

1.The Catastrophe Insurance Scheme to Be Launched at the End of this Year in China

Catastrophe insurance scheme is expected to launch at the end of 2010，which will establish catastrophe fund in each province instead of a national unified one.Admittedly，China has many provinces and the economic levels and main natural disasters may be quite different.Is this reasonable that each province establishing its own catastrophe fund?

Suppose that there are two different provinces R1 and R2， e is its economic level，c is one kind of catastrophe a province suffers，p is the probability of the catastrophe occurrence， a is the amount of loss and finally r is the interest rate of the catastrophe fund(catastrophe fund in reinsurance requires low risk，thus all the fund are deposited into bank ).F=R（e，c，p，a，r） is the utility function.

Fi=Ri（ei，ci，pi，ai，ri）i=1，2ci∈C，C={flood，drought，typhoon，earthquake……}e1＞e2，r1＞r2

If economic level is higher，the scale of catastrophe fund is larger，thus the rate of deposit interest is higher.If the two provinces cooperate，then

F=R（e1+e2，c1∪c2，1-（1-p1）*（1-p2），a1+a2，r）r＞r1＞r2

F1=e1*（1+r1）n-a1*p1F2=e2*（1+r2）n-a2*p2

F=（e1+e2）*（1+r）n-a1*p1-a2*p2+p1*p2*（a1+a2）F-F1-F2＞0

Players:R1andR2 Strategies: Cooperate or not cooperate

Payoffs:

K1=*F K2=*F

（K1-F1）＋（K2-F2）＞0 So，at least one ofand is positive.

Analysis:

（1）K1-F1＞0，K2-F2＝0， R1chooses to cooperate and R2 chooses to cooperate.

（2）K1-F1＝0，K2-F2＞0， R1 chooses to cooperate and R2 chooses to cooperate.

（3）K1-F1＞0，K2-F2＜0，R1 chooses to cooperate and R2 chooses to not cooperate.

（4）K1-F1＜0，K2-F2＞0，R1 chooses to not cooperate and R2 chooses to cooperate.

Conclusion: Regional cooperation can share the big catastrophe risk and establishes a harder foundation for catastrophe insurance.But it is the gap of benefit distribution between them that hinders this regional cooperation system.The catastrophe these years shows that in the southwest part of China，where economy level is lower than other region，catastrophe occurs more.If these regions are isolated，their ability to against catastrophe risk is limited，and other regions would pay more for that such as donations for them.Some measures should be taken to encourage regional cooperation in catastrophe insurance fund systems.

2.Tentative Design of Catastrophe Insurance Mechanism in China

Based on the analysis above，a tentative design of catastrophe insurance mechanism in China is established.

（1）Every province sets up its own catastrophe fund.

（2）Put spercent of province fund is as the part of the national catastrophe fund.

（3）Once a province is in catastrophe，the local catastrophe fund would offer the basic losses and the national catastrophe fund would compensate it for c percent of the national catastrophe fund.

（4）If residents buy the commercial catastrophe insurance they just pay k percent of the premium and the local catastrophe fund pays the 1-k percent premium.Once catastrophe occurs，residents would get the commercial catastrophe insurance.

（5）If residents do not buy the commercial catastrophe insurance，once catastrophe occurs，they would just get the losses compensation of the local and national catastrophe fund.

3.Game Analysis of Tentative Design of Catastrophe Insurance Mechanism

Players:

Player1: local catastrophe fund;Player2 : insurance companies;

Player3: residents; Player4: national catastrophe fund

Strategies:

Si={s1g，s2g}Si={s1i=set up，s2i=not set up} Sr={s1r=buy，s2r=not buy} Sn={s1o，s2o}

Payoffs:

Suppose that fi donates the amount of money of catastrophe fund in provincei，than the national catastrophe fund f=∑mi=1sfi . x is the number of residents who purchase commercial catastrophe insurance，total premium is p（x），X is the total number of residents of the province. L is the losses. Lextra is the extra loss which would be compensated by the commercial insurance companies. p is the probability of catastrophe occurring.

L＝cf+（1-s）fi＋LextraUbuy=[cf+（1-s）fi＋Lextra-kp（x）]－k（1-p）p（x）

Unot-buy=P[cf+（1-s）fi]ΔU=Ubuy-Unot-buy=p[Lextra-kp（x）]－k（1-p）p（x）=pLextra-kp（x）

If ΔU＞0，residents tend to buy the commercial catastrophe insurance，else，they will refuse to buy it.But in reality，ΔU＞0 is in general，then people would like to buy this product.Thus，their extra loss especially who has a large property would be compensated in a larger measure.

Uinsuranc companies=p[p（x）-Lextra]+（1-p）p（x）=p（x）-pLextra

Because insurance companies in the game usually get a large premium both from residents and the government， p is very small and the extra losses are not so big，so usually Uinsuranc companies＞0 .Thus insurance companies would like to set up this insurance business.

As for the catastrophe fund，they are all for residents，consequently they are benefit to this game.Therefore this would be an all-win game.

Reference：

[1]Zifa Wang，Tun Lin，and George Walker，2009，Earthquake Risk and Earthquake Catastrophe Insurance for the People’s Republic of China，Asian Development Bank.

[2]China Statistical Yearbook 2009，China Statistics Press.

Game Analysis of Catastrophe Insurance

XU Ru-pei

（College of Operations Research and Management Science，Qufu Normal University，Rizhao 276826，China）

Abstract:Recently，China has witnessed a lot of catastrophe events.Though catastrophe insurance scheme is expected to launch at the end of the year，there is still a long way to cover.This paper aims to analyze the catastrophe insurance mechanism of China with game theory and provides some suggestions to this problem.

Key words: catastrophe insurance；game analysis；insurance mechanism