稳定Hawkes过程下的保险公司分红问题  

Optimal dividend payment in an insurance company with stationary Hawkes process

作　　者：陈亦令 边保军[1] CHEN Yi-ling;BIAN Bao-jun(School of Mathematical Sciences,Tongji University,Shanghai 200092,China)

机构地区：[1]同济大学数学科学学院,上海200092

出　　处：《高校应用数学学报（A辑）》2020年第2期158-168,共11页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11771135)。

摘　　要：引入Hawkes过程来代替经典的泊松过程,建立了索赔具有族群特性的一类保险公司分红模型,并探究了最优分红策略问题.引入粘性解的概念,利用动态规划原理推导出优化问题,其解满足一个完全非线性偏微分方程:Hamilton-Jacobi-Bellman方程,并证明了值函数是相关方程的粘性解,给出了验证定理.最后进行数值模拟实验,并介绍了障碍线策略实施过程.The optimal dividend payment problem in an insurance company whose surplus follows the classical Cramér-Lundberg process with cluster claims is considered.A Hawkes process is introduced so that the occurrence of a claim in the risky asset price triggers more sequent jumps.Using dynamic programming principle and viscosity solution theory,it shows that the optimal value function is a viscosity solution of the associated Hamilton-Jacobi-Bellman(HJB)equation.The optimal value function can be characterized as the smallest viscosity supersolution of the HJB equation.Finally,some numerical results are exhibited and a barrier line strategy is introduced.

关 键 词：保险 最优分红 Hawkes过程 粘性解 障碍线策略 

分 类 号：F840[经济管理—保险]