基于CRRA效用准则的两类索赔保险与再保险决策  

Two Classes of Claims Insurance and Reinsurance Strategies Based on CRRA Utility Criteria

作　　者：陈冉 江五元[1] 杨佳悦 CHEN Ran;JIANG Wu-yuan;YANG Jia-yue(Department of Mathematics,Hunan Institute of Science and Technology,Yueyang 414006,China)

机构地区：[1]湖南理工学院数学学院,湖南岳阳414006

出　　处：《数学的实践与认识》2024年第6期31-42,共12页Mathematics in Practice and Theory

基　　金：湖南省社科评审委项目(XSP24YBZ057);湖南省教育厅重点项目(23A0490)。

摘　　要：研究了在两类风险索赔影响下保险人的稳健最优投资与再保险策略问题.保险人将盈余分别投资于无风险债券、股票以及期权,其目标是终端财富在幂效用(CRRA)下最大化.假设风险资产价格服从Heston随机波动率模型,此外保险人还可以购买比例再保险来分散投资风险.利用随机最优控制理论,得到了稳健最优再保险、投资策略以及值函数的解析表达式.最后,通过数值模拟分析了模型参数对最优策略的影响.This paper mainly studies the insurer's robust optimal investment and reinsurance strategies under two classes of risk claims.The insurer is allowed to invest in a risk-free bond,a stock and an option.The objective is to maximize the power utility of net wealth at the end of time.The stock is subject to Heston stochastic volatility model,and insurer can buy proportional reinsurance to diversify investment risks.Using stochastic optimal control theory,the analytic expressions of robust optimal reinsurance,investment strategies and value function are obtained.Finally,the influences of the model parameters on the optimal strategies are analyzed by numerical simulation.

关 键 词：两类索赔 Heston模型 期权 模糊厌恶 稳健策略 

分 类 号：F840[经济管理—保险] O232[理学—运筹学与控制论]