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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (11): 1-14,26.doi: 10.6040/j.issn.1671-9352.0.2022.265

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基于Stackelberg博弈的最优再保险合同设计

杨鹏1(),张晓燕2   

  1. 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
  • 收稿日期:2022-04-29 出版日期:2023-11-20 发布日期:2023-11-07
  • 作者简介:杨鹏(1983—), 男, 副教授, 博士, 研究方向为再保险和风险管理. E-mail: pyang@xaufe.edu.cn
  • 基金资助:
    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)

Optimal reinsurance contract design based on Stackelberg game

Peng YANG1(),Xiaoyan ZHANG2   

  1. 1. School of Mathematics, Xi'an University of Finance and Economics, Xi'an 710100, Shaanxi, China
    2. Xi'an Changfeng Research Institute of Mechanism and Electricity, Xi'an 710065, Shaanxi, China
  • Received:2022-04-29 Online:2023-11-20 Published:2023-11-07

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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。

关键词: 再保险合同, 再保费, 保险业务相依, 相对业绩, Stackelberg博弈

Abstract:

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.

Key words: reinsurance contract, reinsurance premium, insurance business dependence, relative performance, Stackelberg game

中图分类号: 

  • O211.6

图1

再保险公司是否从事保险业务和τ1对最优再保险合同的影响"

图2

再保险公司是否从事保险业务和τ2对最优再保险合同的影响"

图3

再保险公司是否从事保险业务和λ对最优再保险合同的影响"

图4

是否考虑保险业务之间的相依性和λ对最优再保险合同的影响"

图5

保险公司是否考虑竞争和λ对最优再保险合同的影响"

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