随机波动模型和违约风险下具有相对绩效关心的最优再保险投资策略  

Optimal Reinsurance-Investment Strategy with Relative Performance Concerns under Stochastic Volatility Model and Default Risk

作　　者：张欣茹 马世霞[1] 慕蕊 Zhang Xinru;Ma Shixia;Mu Rui(School of Science,Hebei University of Technology,Tianjin 300401,China)

机构地区：[1]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5期30-43,共14页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：Supported by the National Natural Science Foundation of China(12071107)。

摘　　要：研究了在随机波动和违约风险下具有相对绩效的最优再保险和投资问题.假设保险公司允许购买比例再保险,其余额可以投资在由无风险资产、违约债券和价格过程满足平方根因子过程的风险资产组成的金融市场.特别地还考虑到了反馈时间的延迟.然后基于随机控制方法,推导出了最优策略和相应值函数的封闭表达式.最后通过数值实验说明了模型参数对最优再保险和投资策略的影响,对不同目标准则下的最优策略进行了比较,进一步揭示了参数的影响.An optimal reinsurance and investment problem with relative performance under stochastic volatility and default risk are investigated.Assume that proportional reinsurance is allowed and the surplus of the insurer can be allocated to the financial market consisting of the risk-free asset,the default bond and the risky asset whose price process satisfies square root factor process.Particularly,the delay of feedback time is taken into account.Then based on the approach of stochastic control,closed-form expressions of the optimal strategies and the corresponding value functions are derived.Finally,numerical experiments are provided to illustrate how the model parameters affect optimal strategies.Besides,optimal strategies under different objective criteria are compared to further reveal the parameters influences.

关 键 词：平方根因子过程 相对绩效关心 均值方差准则 指数效用 延迟 

分 类 号：O211.6[理学—概率论与数理统计]