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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (1): 20-36.doi: 10.3969/j.issn.1005-3085.2022.01.002

• • 上一篇    下一篇

扩散风险模型下保险公司和再保险公司之间的最优再保险策略选择博弈

林  祥,   朱冠霞,  钱艺平   

  1. 浙江工商大学金融学院，杭州 310018
  • 出版日期:2022-02-15 发布日期:2022-04-15
  • 基金资助:
    教育部人文社科基金 (18YJA790051; 19YJE790001)；浙江省自然科学基金 (LY17A010005)；杭州市哲社规划课题 (Z19JC111).

Optimal Reinsurance Strategy Game between Insurer and Reinsurer for a Diffusion Risk Model

LIN Xiang,   ZHU Guanxia,   QIAN Yiping   

  1. School of Finance, Zhejiang Gongshang University, Hangzhou 310018
  • Online:2022-02-15 Published:2022-04-15
  • Supported by:
    The Humanities and Social Sciences Foundation of the Ministry of Education (18YJA790051; 19YJE790001); the Natural Science Foundation of Zhejiang Province (LY17A010005); the Philosophy Society Planning Project of Hangzhou (Z19JC111).

PDF (PC)

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摘要：

保险公司可以根据再保险价格决定是否购买比例再保险及购买数量，同时再保险公司也可根据再保险价格决定是否承保以及承保数量。一个合理的再保险合约应该同时考虑保险公司和再保险公司的利益。在扩散风险模型下运用动态规划原理研究了保险公司和再保险公司之间的再保险策略选择博弈问题。在保险公司和再保险公司都具有指数效用函数条件下，得到了三种博弈情形下保险公司和再保险公司之间的再保险策略选择问题的显示解。结果显示，在适当的条件下，保险公司和再保险公司的效用都可以得到提高。最后，通过数值计算给出了最优比例再保险策略和再保险保费，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。

关键词: 比例再保险, 再保险保费, 效用最大化, 承保, Hamilton-Jacobi-Bellman 方程

Abstract:

The insurance company can decide whether to purchase a proportional reinsurance according to the reinsurance price, while the reinsurance company can decide whether to accept the reinsurance contract. Then a reinsurance contract should appear as a reasonable compromise between the insurer's and the reinsurer's interest. The paper considers a reinsurance selection game problem between an insurance company and a reinsurance company for a diffusion risk model by invoking the use of the dynamic programming principle. A closed-form solutions of the reinsurance selection game problems is obtained under three cases for the insurance company and the reinsurance company with an exponential utility function. The expected surplus utilities of the insurance company and the reinsurance company can increase under some conditions. Numerical examples are also provided to illustrate how the reinsurance strategy and the reinsurance price, as well as the utility profit change when some model parameters vary.

Key words: proportional reinsurance, reinsurance price, utility maximization, underwriting reinsurance, Hamilton-Jacobi-Bellman

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