基于时滞和多维相依风险模型的最优期望-方差比例再保险  

Optimal mean-variance reinsurance with delay and multiple classes of dependent risks

作　　者：杨潇潇[1] 梁志彬[1] 张彩斌 

机构地区：[1]南京师范大学数学科学学院,南京210023

出　　处：《中国科学：数学》2017年第6期723-756,共34页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11471165);江苏省自然科学基金(批准号:BK20141442);江苏省普通高校研究生科研创新(批准号:KYLX15 0723)资助项目

摘　　要：本文考虑基于时滞和多维复合Poisson相依风险模型的最优比例再保险问题,以最大化终端财富值的期望-方差效用为目标,在博弈论的框架下构建时间不一致问题,并探讨该问题下的子博弈Nash均衡策略.通过随机控制理论以及相应的广义Hamilton-Jacobi-Bellman(HJB)方程,本文得到了保险业务数量n=2情形下最优策略和值函数的显式表达;同时通过降维的方法得到n=3情形下最优结果的解析解,这类降维的方法同样适用于n>3的情形.最后,通过一些数值例子和图表来进一步说明所获得的结论,并探讨模型中某些重要参数对最优结果的影响.In this paper, we consider an optimal proportional reinsurance problem for the compound Poisson risk model with delay and multiple dependent classes of insurance business. Under the criterion of maximizing the mean-variance utility of the terminal wealth, we formulate the time-inconsistent problem within a game theoretic framework and look for a subgame perfect Nash equilibrium strategy. Based on the technique of stochastic control theory and the corresponding extended Hamilton-Jacobi-Bellman equation, the explicit expressions of the optimal equilibrium strategy and the value function are derived for the case of insurance business n - 2. Meanwhile, we derive the closed-form expressions of optimal solutions for the case of n = 3 by the method of dimension reduction which can be used to get the optimal results for the case of n 〉 3. Finally, some numerical examples are presented to show the impact of model parameters on the optimal strategies.

关 键 词：时滞 多维相依风险 期望-方差效用 时齐策略 广义Hamilton-Jacobi-Bellman方程 比例再保险 

分 类 号：O211.67[理学—概率论与数理统计]