基于Stackelberg博弈的最优再保险合同设计  

Optimal reinsurance contract design based on Stackelberg game

作　　者：杨鹏 张晓燕 YANG Peng;ZHANG Xiaoyan(School of Mathematics,Xi'an University of Finance and Economics,Xi'an 710100,Shaanxi,China;Xi'an Changfeng Research Institute of Mechanism and Electricity,Xi'an 710065,Shaanxi,China)

机构地区：[1]西安财经大学数学学院,陕西西安710100 [2]西安长峰机电研究所,陕西西安710065

出　　处：《山东大学学报（理学版）》2023年第11期1-14,26,共15页Journal of Shandong University(Natural Science)

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

摘　　要：针对再保险合同设计问题,即再保费的定价问题,假设市场上有1家保险公司和1家再保险公司,其中,保险公司从事2类保险业务,再保险公司从事1类保险业务。为了体现保险公司与再保险公司之间的竞争,假设3类保险业务具有相依性,且允许保险公司从事再保险业务。利用相对业绩,量化保险公司与再保险公司之间的竞争。保险公司和再保险公司的目标都是寻找最优的再保险合同,最大化它们终端财富的均值同时最小化其方差。在Stackelberg博弈框架下,通过使用随机分析和随机控制理论,求得最优再保险合同和值函数的显式解。最终,通过数值实验分析模型参数对最优再保险合同的影响,比较一些特殊情形与一般情形的关系。For the optimal reinsurance contract design problem,that is,the reinsurance premium pricing problem,we assume that there is an insurance company and a reinsurance company on the market.Among them,the insurance company is engaged in two types of insurance business,and the reinsurance company is engaged in one type of insurance business.To reflect the competition between the insurance company and the reinsurance company,we assume that these three insurance businesses are interdependent,and the insurance company can engage in the reinsurance business.Using the relative performance,the competition between the insurance company and the reinsurance company is quantified.The aims of the insurance company and the reinsurance company are to find an optimal reinsurance contract to maximize the mean of the terminal wealth and minimize the variance of the terminal wealth.Under the Stackelberg game framework,by using stochastic calculus and stochastic control theory,the explicit solutions for the optimal reinsurance contract and the optimal value function are obtained.Finally,the influence of model parameters on the optimal reinsurance contract is analyzed through numerical experiments and the relationship between some special cases and general cases is compared.

关 键 词：再保险合同 再保费 保险业务相依 相对业绩 STACKELBERG博弈 

分 类 号：O211.6[理学—概率论与数理统计] F840[理学—数学]