保险公司和再保险公司之间的停止损失再保险策略选择博弈  

The Excess-of-Loss Reinsurance Strategy Selection Game Between an Insurer and a Reinsurer

作　　者：林祥[1] 钱艺平 任余豪 LIN Xiang;QIAN Yiping;REN Yuhao(School of Finance,Zhejiang Gongshang University,Hangzhou 310018,China)

机构地区：[1]浙江工商大学金融学院,浙江杭州310018

出　　处：《应用数学》2021年第2期463-476,共14页Mathematica Applicata

基　　金：浙江省自然科学基金(LY17A010005);教育部人文社科基金(18YJA790051,19YJE790001);浙江省软科学研究计划项目(2019C35064)。

摘　　要：本文在扩散逼近风险模型下考虑保险公司和再保险公司之间的停止损失再保险策略选择博弈问题.假设保险公司和再保险公司都以期望终端盈余效用增加作为购买停止损失再保险和接受承保的条件.在保险公司和再保险公司都具有指数效用函数条件下,运用动态规划原理,通过求解其对应的Hamilton-Jacobi-Bellman方程,得到了三种博弈情形下保险公司和再保险公司之间的停止损失再保险策略和值函数的显示解,以及再保险合约能够成交时再保费满足的条件.结果显示,在适当的条件下,保险公司和再保险公司之间的停止再保险合约是可以成交的.最后,通过灵敏性分析给出了最优停止损失再保险策略和再保费,以及效用损益与模型主要参数之间的关系,并给出相应的经济分析.In this paper we investigate the excess-of-loss reinsurance strategy selection game problem between an insurer and a reinsurer for a diffusion approximation risk model.Suppose that both the insurer and the reinsurer take the increase of expected terminal surplus utility as the conditions for purchasing the excess-of-loss reinsurance and underwriting reinsurance.By invoking the use of the dynamic programming principle and solving the corresponding Hamilton-Jacobi-Bellman equations,we obtain closed-form solutions of the excess-of-loss reinsurance selection game problems between the insurer and the reinsurer under three cases for the insurer and the reinsurer with an exponential utility function.The results show that the excess-of-loss reinsurance contract can be signed between the insurer and the reinsurer under some appropriate conditions.Finally,sensitivity analyses are also provided to illustrate how the optimal excess-of-loss strategy and the reinsurance premium and the utility profit change when some model parameters vary.

关 键 词：停止损失再保险 承保 指数效用函数 HAMILTON-JACOBI-BELLMAN方程 效用损益 

分 类 号：O211.67[理学—概率论与数理统计]