具有状态依赖风险规避和非卖空约束的最优再保险和投资策略  

Optimal Reinsurance and Investment Strategies with State Dependent Risk Aversion and No-shorting Constraint

作　　者：靳冰岩 吴梦虹 马世霞[2] Jin Bingyan;Wu Menghong;Ma Shixia(Xishan Campus of Shijiazhuang No.1 High School,Shijiazhuang 050000 China;School of Science,Hebei University of Technology,Tianjin 300401,China)

机构地区：[1]石家庄一中西山学校,河北石家庄050000 [2]河北工业大学理学院,天津300401

出　　处：《南开大学学报（自然科学版）》2022年第3期44-54,共11页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：Supported by NSFC(12071107)。

摘　　要：研究了在跳扩散金融市场下具有状态依赖风险规避和非卖空约束的最优再保险和投资问题.假定保险公司盈余过程是由复合泊松过程表示,两个跳跃过程是由共同的冲击引起的.特别地,当风险规避动态地取决于当前财富时模型更真实.在均值-方差准则下,在博弈论的框架内制定了时间不一致的问题,并寻求子博弈完美的纳什均衡策略.通过应用随机控制方法可以明确得出最优的再保险和投资策略.最后提供一些数值例子说明了模型参数对最优结果的影响.An optimal reinsurance and investment problem is investigated in a jump-diffusion financial market with state dependent risk aversion and no-shorting constraint.Assume that the insurance risk process is driven by a compound Poisson process and the two jump number processes are correlated by a common shock.In particular,when the risk aversion depends dynamically on current wealth,the model is more realistic.Under the mean variance criterion,the problem of time inconsistency is formulated within the framework of game theory,and the perfect Nash equilibrium strategy of subgame is sought.By applying stochastic control approach,the optimal reinsurance and investment strategies explicitly are derived.Finally,some numerical examples are presented to show the impact of model parameters on the optimal results.

关 键 词：最优再保险和投资 跳扩散模型 状态依赖风险规避 非卖空约束 

分 类 号：O211.6[理学—概率论与数理统计]