损失依赖保费下的稳健最优投资和再保险策略  

Robust Optimal Investment and Reinsurance Strategy under Loss-dependent Premium Principle

作　　者：苏毅明 陈密[1,2] SU Yi-ming;CHEN Mi(School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,China;Fujian Provincial Key Laboratory of Analytical Mathematics and Applications,Fuzhou 350117,China)

机构地区：[1]福建师范大学数学与统计学院,福建福州350117 [2]福建省分析数学及应用重点实验室,福建福州350117

出　　处：《兰州文理学院学报（自然科学版）》2024年第2期8-14,共7页Journal of Lanzhou University of Arts and Science(Natural Sciences)

基　　金：国家自然科学基金(11701087);福建省自然科学基金(2023J01537,2023J01538)。

摘　　要：探究了在最大化终端期望指数效用准则下保险人的稳健最优投资和再保险问题.其中,保险人采用了损失依赖保费原则,而再保险人由于信息不对称仍采用期望保费原则,风险投资由GBM模型刻画.通过动态规划原理处理稳健优化问题后可得到稳健最优投资和再保险策略以及相应的值函数.最后,用数值模拟验证参数对最优策略的影响.This paper investigates the problem of robust optimal investment and reinsurance for insurers under the criterion of maximizing the terminal expected exponential utility.The insurer adopts the loss-dependent premium principle,while the reinsurer,due to asymmetric information,still uses the expected premium principle.Risk investment is characterized by the GBM model.By applying the dynamic programming principle to handle the problem of robust optimization,the robust optimal investment and reinsurance strategies,as well as the corresponding value function,can be obtained.Finally,numerical simulations are conducted to demonstrate the impact of parameters on the optimal strategies.

关 键 词：再保险和投资 损失依赖保费 指数效用最大化 不确定模型 

分 类 号：O211.6[理学—概率论与数理统计]