均值回复市场中的最优再保险与投资决策

上海交通大学学报（自然版） ›› 2013, Vol. 47 ›› Issue (03): 438-443.

均值回复市场中的最优再保险与投资决策

王蕾，顾孟迪

（上海交通大学安泰经济与管理学院，上海 200052）

收稿日期:2012-05-25 出版日期:2013-03-28 发布日期:2013-03-28
基金资助:
上海交通大学文理交叉专项基金资助项目（10JCY11）

Optimal Reinsurance-Investment Strategies in a Mean-Reverting Market

WANG Lei, GU Meng-Di

(Antai College of Economics and Management, Shanghai Jiaotong University, Shanghai 200052, China)

Received:2012-05-25 Online:2013-03-28 Published:2013-03-28

摘要/Abstract

摘要： 假定风险资产价格服从均值回复的指数OU过程（Schwartz模型），而索赔服从带漂移的随机布朗运动，利用随机控制原理分别探讨了幂效用和指数效用保险人的最优再保险与投资策略，并运用数值算例模拟了设定条件下均值回复速率与最优投资策略的关系.结果表明，在含有均值回复特性的市场环境中，最优策略不仅依赖于时间和财富的瞬时绝对量，还依赖于风险资产的现货价格对均值的偏离水平.资产价格的可预测性要求决策者要判断市场发展的不同阶段，针对市场趋势制定不同的投资策略.

关键词: 再保险, 投资, 均值回复, 最优策略, 随机控制

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

中图分类号:

F 840.3

王蕾, 顾孟迪. 均值回复市场中的最优再保险与投资决策[J]. 上海交通大学学报（自然版）, 2013, 47(03): 438-443.

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.

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