CEV模型下保险公司的最优不动产投资及再保险问题  

Optimal real estate investment and reinsurance problem for an insurer under a CEV model

作　　者：李国庆 田琳琳 LI Guoqing;TIAN Linlin(College of Science,Donghua University,Shanghai,China)

机构地区：[1]东华大学理学院,上海

出　　处：《东华大学学报（自然科学版）》2024年第1期178-185,共8页Journal of Donghua University(Natural Science)

基　　金：国家自然科学基金青年科学基金项目(12201104);中央高校基本科研业务费专项资金(2232021D-29)。

摘　　要：针对保险公司的最优效用问题,在以往债券、股票及最优再保险的投资组合基础上,分析不动产及出租该不动产所获得的随机收益模型,研究保险公司不动产的最优投资组合及最优再保险策略。通过动态规划原理,建立Hamilton-Jacobi-Bellman方程,解得最优投资、再保险策略以及最优值函数的显式解,通过验证定理证明Hamilton-Jacobi-Bellman方程的经典解析解是最优值函数。研究结果量化了时间、财富值、利率、股票价格等变量对于最优策略及公司效用的影响,具有一定的经济学意义。To study the optimal utility problem of insurance companies,based on previous literatures about the investment portfolios of bonds,stocks and optimal reinsurance,the real estate and the stochastic income model received by leasing the real estate were analyzed,and the optimal investment portfolio and optimal reinsurance strategy with real estate were derived.By the dynamic programming principle and solving establishing the Hamilton-Jacobi-Bellman equation,solving the explicit expression solution of the optimal investment,reinsurance policy strategy and optimal function were obtained.Meanwhile value function,by the verification theorem,the classical solution of the Hamilton-Jacobi-Bellman equation was shown to be the optimal value function.The research results quantify the impact of variables such as time,wealth value,interest rates,and stock prices on the optimal strategy and company utility,which has certain economic significance.

关 键 词：CEV模型 不动产模型 HAMILTON-JACOBI-BELLMAN方程 指数效用 验证定理 

分 类 号：O211.9[理学—概率论与数理统计]