突发事件影响下的最优再保险和投资策略  

Optimal Reinsurance and Investment Strategy under the Influence of Unexpected Events

作　　者：杨鹏 YANG Peng(School of Mathematics,Xi'an University of Finance and Economics,Xi'an,710100,China)

机构地区：[1]西安财经大学数学学院,西安710100

出　　处：《应用概率统计》2024年第4期525-542,共18页Chinese Journal of Applied Probability and Statistics

基　　金：陕西省自然科学基础研究计划(批准号:2023-JC-YB-002);教育部人文社会科学研究西部和边疆地区项目(批准号:21XJC910001)资助.

摘　　要：本文研究了在突发事件影响下,最优时间一致的再保险和投资问题.保险人经营n类保险业务,受到突发事件影响后,n类保险业务产生相互影响,同时保险业务与风险资产的价格之间也产生相互影响.针对每类保险业务,保险人通过再保险减少索赔风险.此外,保险人还通过在金融市场投资来增加财富.金融市场由一个无风险资产和一个风险资产组成,风险资产的价格满足跳−扩散过程.本文的主要研究目标是,寻找最优时间一致的再保险和投资策略最大化终值财富的均值,同时最小化终值财富的方差.通过使用随机控制和随机最优优化技术,我们建立了推广的Hamilton-Jacobi-Bellman(HJB)方程.进而,通过求解推广的HJB方程,我们得到了最优时间一致的再保险和投资策略以及相应值函数的显式解,并从理论上探讨了最优策略的经济意义.最终,通过数值实验分析了突发事件对最优时间一致的再保险和投资策略的影响,得到了一些深刻的经济见解.This paper studies an optimal time-consistent reinsurance and investment problem under the influence of unexpected events.An insurer operates n insurance businesses,and after being affected by the unexpected events,n insurance businesses have interaction,meanwhile,the insurance business and the price of risky asset also have interaction.For each type of insurance business,the insurer reduces the claim risk through reinsurance.In addition,the insurer also increases his wealth by investing in the financial market.The financial market consists of a risk-free asset and a risky asset,and the price of the risky asset satisfies a jump-diffusion process.The main research goal of this paper is to find an optimal time-consistent reinsurance and investment strategy so as to maximize the expected terminal wealth while minimizing the variance of the terminal wealth.By using the stochastic control and stochastic optimization techniques,we establish the extended Hamilton-Jacobi-Bellman(HJB)equation.Explicit solutions for the optimal time-consistent reinsurance and investment strategy as well as the corresponding value function are obtained by solving the extended HJB equation,and the economic significance of the optimal strategy is discussed theoretically.Finally,numerical experiments are conducted to illustrate the effects of unexpected events on the optimal time-consistent reinsurance and investment strategy,and some meaningful economic insights or implications are provided.

关 键 词：突发事件 再保险 投资 随机控制 推广的HJB方程 

分 类 号：O211.63[理学—概率论与数理统计]