竞争与合作统一框架下的鲁棒最优再保险策略  

Robust Optimal Reinsurance Strategy Under the Unified Framework of Competition and Cooperation

作　　者：杨鹏 YANG Peng(School of Mathematics,Xi'an University of Finance and Economics,Xi'an 710100)

机构地区：[1]西安财经大学数学学院,西安710100

出　　处：《系统科学与数学》2023年第5期1260-1275,共16页Journal of Systems Science and Mathematical Sciences

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

摘　　要：在实际中,多个保险人之间经常存在竞争与合作.文章在竞争与合作统一框架下,研究了鲁棒最优再保险策略.每个保险人的盈余过程满足扩散逼近保险模型,n个保险人的索赔之间存在相依关系,每个保险人通过再保险减少索赔风险.文章主要的研究目标是,在最坏市场环境下,寻找最优均衡再保险策略最大化终端财富的均值同时最小化其方差.通过使用随机动态规划和随机控制理论,求得了鲁棒最优均衡再保险策略、最优市场策略和最优值函数的显式解,并从理论上探讨了最优策略的经济意义.最终,通过数值实验分析了竞争、合作、模糊厌恶和风险厌恶对鲁棒最优均衡再保险策略的影响.文章的研究结果可以有效地指导保险人的实践.In practice,there is often competition and cooperation among many insurers.Under the unified framework of competition and cooperation,this paper studies the robust optimal reinsurance strategy.The surplus process of each insurer satisfies the diffusion approximation insurance model,and the claims of n insurers are interdependent,and each insurer reduces the claim risk through reinsurance.The main research aim of this paper is to find the optimal equilibrium reinsurance strategy to maximize the mean of terminal wealth and minimize its variance in the worst market environment.By using stochastic dynamic programming and stochastic control theory,the explicit solutions of robust optimal equilibrium reinsurance strategy,optimal market strategy and optimal value function are obtained,and the economic significance of the optimal strategy is discussed theoretically.Finally,the influence of competition,cooperation,ambiguity aversion and risk aversion on the robust optimal equilibrium reinsurance strategy is analyzed by numerical experiments.The research results can effectively guide the practice of insurers.

关 键 词：随机优化 模糊厌恶 竞争 合作 再保险 

分 类 号：F840.6[经济管理—保险] F224