Optimal Reinsurance-Investment Strategies in a Mean-Reverting Market

Abstract

Abstract: In a mean-reverting market, how to arrange reinsurance and investment proportions is a practical problem faced by general insurers. Assuming that the price of the risky asset is simulated by the exponential OrnsteinUhlenbeck process and the claim process follows a Brownian motion with drift, the optimal proportional reinsurance and investment decisions for insurers with power utility or exponential utility function were studied by stochastic control. A numerical simulation was presented to illustrate the relationship between the speed of mean-reversion and the optimal investment strategy. The results indicate that in a meanreverting market, the optimal strategy depends on not only time and wealth but also the extent of the spot price of the risky asset deviating from the mean value. The predictability of prices requires decision makers to judge the market stage and decide investment strategy in the light of market trend. Key words：

Key words: investment, mean-reversion, optimal strategies, stochastic control, reinsurance

CLC Number:

F 840.3

WANG Lei, GU Meng-Di. Optimal Reinsurance-Investment Strategies in a Mean-Reverting Market[J]. Journal of Shanghai Jiaotong University, 2013, 47(03): 438-443.

References

［1］Promislow D S, Young V R. Minimizing the probability of ruin when claims follow Brownian motion with drift［J］. North American Actuarial Journal, 2005, 9(3): 109128.
［2］Cao Y, Wan N. Optimal proportional reinsurance and investment based on HamiltonJacobiBellman equation［J］. Insurance: Mathematics and Economics, 2009, 45(2): 157162.
［3］Gu M, Yang Y, Li S, et al. Constant elasticity of variance model for proportional reinsurance and investment strategies［J］. Insurance: Mathematics and Economics, 2010, 46(3): 580587.
［4］郭文旌，李心丹. 最优保险投资决策［J］. 管理科学学报，2009,12（1）:118124.
GUO Wenjing, LI Xindan. Optimal investment decision of insurer［J］. Journal of Management Sciences in China, 2009,12(1):118124.
［5］梁志彬，郭军义.最优比例与超额损失组合再保险下的破产概率［J］.数学学报，2010,9(5)： 857870.
LIANG Zhibin, GUO Junyi. Ruin probabilities under optimal combining quotashare and excess of loss reinsurance［J］. Acta Mathematica Sinica, 2010,9(5):857870.
［6］Bali T G, Demirtas K O, Levy H. Nonlinear mean reversion in stock prices［J］. Journal of Banking & Finance, 2008, 32(5): 767782.
［7］Cunado J, GilAlana L A, Gracia F P. Mean reversion in stock market prices: New evidence based on bull and bear markets［J］. Research in International Business and Finance, 2010, 24(2): 113122.
［8］Schwartz E S. The stochastic behaviour of commodity prices: Implications for valuation and hedging［J］. The Journal of Finance, 1997, 52(3): 923973.
［9］Benth F E, Karlsen K H. A note on Merton’s portfolio selection problem for the Schwartz meanreversion model［J］. Stochastic Analysis and Applications, 2005, 23(4): 687704.
［10］Fleming W H, Soner H M. Controlled markov process and viscosity solutions［M］. 2nd ed. New York: Spring, 2005.

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