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高校应用数学学报
高校应用数学学报  2020, Vol. 35 Issue (2): 158-168    
    
稳定Hawkes过程下的保险公司分红问题
陈亦令, 边保军
同济大学 数学科学学院, 上海 200092
Optimal dividend payment in an insurance company with stationary Hawkes process
CHEN Yi-ling, BIAN Bao-jun
School of Mathematical Sciences, Tongji University, Shanghai 200092
 全文: PDF(322 KB)  
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.
关键词： 保险;  最优分红;  Hawkes过程;  粘性解;  障碍线策略    
Abstract: The optimal dividend payment problem in an insurance company whose surplus follows the classical Cram′er-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.
Key words: insurance    optimal dividend payment    Hawkes process    viscosity solution    barrier line strategy
出版日期: 2020-07-07
CLC:  F840  
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陈亦令
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引用本文:

陈亦令, 边保军. 稳定Hawkes过程下的保险公司分红问题[J]. 高校应用数学学报, 2020, 35(2): 158-168.

CHEN Yi-ling, BIAN Bao-jun. Optimal dividend payment in an insurance company with stationary Hawkes process. Applied Mathematics A Journal of Chinese Universities, 2020, 35(2): 158-168.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2020/V35/I2/158

[1] 张节松, 肖庆宪. 方差分保费原则下相依多险种模型的最优再保险[J]. 高校应用数学学报, 2016, 31(3): 253-261.