指数保费准则下的最优投资和比例再保险

Abstract

Abstract:

This paper studies the optimal investment and proportional reinsurance policies of an insurer whose insurance business follows a diffusion perturbed classical risk process. It is assumed that the reinsurance premium is calculated according to the exponential premium principle which makes the stochastic control problems to be nonlinear. The problems of maximizing the adjustment coefficient and the expected exponential utility of terminal wealth are considered.
In both of the problems, explicit expressions for their optimal value functions and the corresponding optimal strategies are obtained. Furthermore, the influences of the risk aversion of the reinsurance company and the uncertainty of the insurance company on the optimal strategies are analyzed.

Key words: Investment, Proportional reinsurance, Exponential premium principle, Adjustment coefficient, Exponential utility

CLC Number:

60J75

CHEN Mi, GUO Jun-Yi. Optimal Investment and Proportional Reinsurance under Exponential Premium Calculation[J].Acta mathematica scientia,Series A, 2014, 34(5): 1161-1172.

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References

[1] Browne S. Optimal investment policies for a firm with random risk process: exponential utility and minimizing the probability of ruin. Mathematics of Operations Research, 1995, 20: 937--958

[2] Hipp C, Plum M. Optimal investment for insurers. Insurance: Mathematics and Economics, 2000, 27: 215--228

[3]  Hipp C, Plum M. Optimal investment for investors with state dependent income, and for insurers. Finance and
Stochastics, 2003, 7: 299--321

[4]  Gaier J, Grandits P, Schachermeyer W. Asymptotic ruin probabilities and optimal investment. Annals of Applied
Probability, 2003, 13: 1054--1076

[5]  Liu C, Yang H. Optimal investment for a insurer to minimize its probability of ruin. North American Acruarial Journal, 2004, 8(2): 11--31

[6]  Yang H, Zhang L. Optimal investment for insurer with jump-diffusion risk process. Insurance: Mathematics and
Economics, 2005, 37: 615--634

[7]  H\o gaard B, Taksar M. Optimal proportional reinsurance policies for diffusion models. Scandinavian Actuarial Journal, 1998, 2: 166--180

[8]  H\o gaard B, Taksar M. Optimal proportional reinsurance policies for diffusion models with transaction costs. Insurance: Mathematics and Economics, 1998, 22: 41--51

[9]  Schmidli H. Optimal proportional reinsurance policies in a dynamic setting. Scandinavian Actuarial Journal, 2001, 1: 55--68

[10]  Taksar M, Markussen C. Optimal dynamic reinsurance policies for large insurance portfolios. Finance and Stochastics, 2003, 7: 97--121

[11]  Liang Z B, Guo J Y. Optimal proportional reinsurance and ruin probability. Stochastic Models, 2007, 23(2): 333--350

[12]  Schmidli H. On minimizing the ruin probability by investment and reinsurance. Annals of Applied Probability, 2002, 12: 890--907

[13]  Schmidli H. Asymptotics of ruin probabilities for risk processes under optimal reinsurance policies: the small claims case. Journal Queueing Systems: Theory and Applications, 2004, 46(1/2): 149--157

[14]  Irgens C, Paulsen J. Optimal control of risk exposure, reinsurance and investments for insurance portfolios.
Insurance: Mathematics and Economics, 2004, 35(1): 21--51

[15]  Bai L H, Guo J Y. Optimal proportional reinsurance and investment with multiple risky assets and no-shorting
constraint. Insurance: Mathematics and Economics, 2008, 42(3): 968--975

[16]  Cao Y, Wan N. Optimal proportional reinsurance and investment based on Hamilton-Jacobi-Bellman equation.
Insurance: Mathematics and Economics, 2009, 45: 157--162

[17]  Zhang X, Zhang K, Yu X. Optimal proportional reinsurance and investment with transaction costs, I: maximizing
the terminal wealth. Insurance: Mathematics and Economics, 2009, 44: 473--478

[18]  Liang Z B, Bai L H, Guo J Y. Optimal investment and proportional reinsurance with constrained control variables.
Optimal Control Applications and Methods, 2011, 32(5): 587--608

[19]  Liang Z B, Yuen K, Guo J Y. Optimal proportional reinsurance and investment in a stock market with Ornstein-Uhlenbeck process. Insurance: Mathematics and Economics, 2011, 49: 207--215

[20]  Young V. Optimal insurance under Wang's premium principle. Insurance: Mathematics and Economics, 1999, 25: 109--122

[21]  Kaluszka M. Optimal reinsurance under mean-variance premium principles. Insurance: Mathematics and Economics, 2001, 28: 61--67

[22]  Kaluszka M. Optimal reinsurance under convex principles of premium calculation. Insurance: Mathematics and Economics, 2005, 36: 375--398

[23]  Zhou M, Yuen K. Optimal reinsurance and dividend for a diffusion model with capital injection: Variance premium principle. Economic Modelling, 2012, 29(2): 198--207

[24]  Musiela M, Zariphopoulou T. An example of indifference prices under exponential preferences. Finance and Stochastics, 2004, 8: 229--239

[25]  Young V, Zariphopoulou T. Pricing dynamic insurance risks using the principle of equivalent utility. Scandinavian Actuarial Journal, 2002, 4: 246--279

[26]  Young V. Equity-indexed life insurance: pricing and reserving using the principle of equivalent utility. North American Actuarial Journal, 2003, 7(1): 68--86

[27]  Moore K, Young V. Pricing equity-linked pure endowments via the principle of equivalent utility. Insurance: Mathematics and Economics, 2003, 33(3): 497--516

[28]  Chen M, Peng X F, Guo J Y. Optimal dividend problem with a nonlinear regular-singular stochastic control.
Insurance: Mathematics and Economics, 2013, 52(3): 448--456

[29]  Centeno M. Measuring the effects of reinsurance by the adjustment coefficient in the Sparre Anderson model. Insurance: Mathematics and Economics, 2002, 30: 37--49

[30]  Hald M, Schmidli H. On the maximisation of the adjustment coefficient under poportional reinsurance. ASTIN Bulletin, 2004, 34: 75--83

[31]  Guerraa M, Centeno M. Optimal reinsurance policy: The adjustment coefficient and the expected utility criteria. Insurance: Mathematics and Economics, 2008, 42: 529--539

[32]  Centeno M, Guerra M. The optimal reinsurance strategy-the individual claim case. Insurance: Mathematics and Economics, 2010, 46: 450--460

[33]  Fleming W, Soner H. Controlled Markov Processes and Viscosity Solutions. New York: Springer, 1993

[34]  Rolski T, et al. Stochastic Processes for Insurance and Finance. Chichester: Wiley, 1999

Optimal Investment and Proportional Reinsurance under Exponential Premium Calculation

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