本文研究了n个合作的保险人与一个再保险人之间竞争下的最优再保险合同制定问题.再保险合同由索赔风险分担策略和再保险价格构成.n个保险人完全相信各自的盈余过程,而再保险人认为每个保险人的盈余过程存在不确定性.每个保险人的目标是,寻找最优的索赔风险分担策略最大化他的终值财富的均值同时最小化其方差.再保险人的目标是,在盈余过程出现最坏情形下,寻找鲁棒最优再保险价格最大化他的终值财富的均值同时最小化其方差.在Stackelberg博弈框架下,通过使用随机控制和随机动态规划技术得到了最优的索赔风险分担策略和再保险价格的显式解,进而得到了最优再保险合同的显式解.最终,通过数值实验解释了模型参数对所得理论结果的影响,得到了一些新的再保险启示.
Abstract
This paper investigates an optimal reinsurance contract formulation problem under the competition between n cooperative insurers and one reinsurer. The reinsurance contract consists of claim risk sharing strategy and reinsurance price. n insurers fully believe in their respective surplus process, while the reinsurer believes that each insurer's surplus process is uncertain. Each insurer's goal is to find an optimal claim risk sharing strategy so as to maximize the expected terminal wealth while minimizing the variance of the terminal wealth. The reinsurer's goal is to find an optimal reinsurance price so as to maximize the expected terminal wealth while minimizing the variance of the terminal wealth under the worst-case scenario of surplus process. Under the Stackelberg game framework, by using the stochastic control and stochastic dynamic programming techniques, we obtain the explicit solutions for the optimal claim risk sharing strategy and reinsurance price, furthermore derive the explicit solution for the optimal reinsurance contract. Finally, the influence of model parameter on the theoretical results is illustrated by numerical experiment, and some new reinsurance inspirations are obtained.
关键词
竞争 /
合作 /
模型不确定 /
索赔风险分担策略 /
再保险价格
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Key words
competition /
cooperation /
model uncertainty /
claim risk sharing strategy /
reinsurance price
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中图分类号：
O225
O211
F840
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基金
教育部人文社会科学研究青年基金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)
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