Acta mathematica scientia, Series B >
THE OPTIMAL STRATEGY FOR INSURANCE COMPANY UNDER THE INFLUENCE OF TERMINAL VALUE
Received date: 2008-12-29
Revised date: 2010-03-27
Online published: 2011-05-20
Supported by
Supported by Doctor Foundation of Xinjiang University and the National Natural Science Foundation of China.
This paper considers a model of an insurance company which is allowed to invest a risky asset and to purchase proportional reinsurance. The objective is to find the policy which maximizes the expected total discounted dividend pay-out until the time of bankruptcy and the terminal value of the company under liquidity constraint. We find the solution of this problem via solving the problem with zero terminal value. We also analyze the influence of terminal value on the optimal policy.
Key words： proportional reinsurance; terminal value; optimal policy; HJB equation
LIU Wei , YUAN Hai-Li , HU Yi-Jun . THE OPTIMAL STRATEGY FOR INSURANCE COMPANY UNDER THE INFLUENCE OF TERMINAL VALUE[J]. Acta mathematica scientia, Series B, 2011 , 31(3) : 1077 -1090 . DOI: 10.1016/S0252-9602(11)60299-3
[1] 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: 968--975
[2] Cvitani\'{c} J, Karatzas I. Convex duality in constrained portfolio optimization. Annals of Applied Probability, 1992, 2(4): 767--818
[3] De Finetti B. Su un'impostazione alternativa dell teoria colletiva del rischio. Transactions of the XV International Congress
of Actuaries, 1957, 2: 433--443
[4] Fleming W H, Soner H M. Controlled Markov Process and Viscosity Solutions. New York: Springer-Verlag, 1993
[5] Gerber H U, Shiu E S W. Optimal dividends: Analysis with Brownian motion. North American Actuarial Journal, 2004, 8(1): 1--20
[6] Grossman S J, Vila J-L. Optimal dynamic trading with leverge constraint. Journal of Financial and Quantitative Analysis, 1992, 27(2): 151--168
[7] HΦjgaard B, Taksar M. Controlling risk eaposure and dividends payout schemes: insurance company example. Mathematical
Finance, 1999, 2: 153--182
[8] HΦjgaard B, Taksar M. Optimal risk control for a large corporation in the presence of returns on investments. Finance Stochast, 2001, 5: 527--547
[9] HΦjgaard B, Taksar M. Optimal dynamic portfolio secetion for a corporation with controllable risk and dividend distribution policy. Quantitative Finance, 2004, 4: 315--327
[10] Lions P, Sznitman A. Stochastic differential equations with reflecting boundary conditions. Communications on Pure and
Applied Mathematics, 1984, 37(4): 511--537
[11] Luo S Z, Taksar M, Tosi A. On reinsurance and investment for large insurance portfolios. Insurance: Mathematics and
Economics, 2008, 42: 434--444
[12] Paulsen J, Gjessing H K. Optimal choice of dividend barriers for risk process with stochastic return of investment. Insurance: Mathematics and Economics, 1997, 20: 215--223
[13] Taksar M. Dependence of optimal risk control decisions on the terminal value for a financial corporation. Annals of Operations
Research, 2000, 98: 89--99
[14] Taksar M. Optimal risk and dividend distribution control models for an insurance company. Mathematical Methods of Operations
Research, 2000, 51: 1--42
[15] Taksar M, Hunderup C L. The influence of bankrupy value on optimal risk control for diffusion models with proportional
reinsurance. Insurance: Mathematics and Economics, 2007, 40: 311--321
[16] Tepl\'{a} L. Optimal portfolio policies with borrowing and shortsale constraints. Journal of Economic Dynamics and Control, 2000, 24: 1623--1639
[17] Yuan H L, Hu Y J. Optimal proportional reinsurance with constant divident barrier. Acta Mathematica Scientia, 2010, 30B(3): 791--798
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