索赔相依下兼顾保险人和再保险人共同利益的鲁棒再保险和投资  

Robust Optimal Reinsurance and Investment Toward Joint Interests of the Insurer and the Reinsurer Under Correlated Claims

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

机构地区：[1]西安财经大学数学学院,西安710100

出　　处：《应用数学学报》2024年第5期721-738,共18页Acta Mathematicae Applicatae Sinica

基　　金：教育部人文社会科学研究一般项目(批准号:21XJC910001)资助。

摘　　要：本文基于期望效用最大化准则,研究再保险和投资问题.市场上有一个保险人和一个再保险人.通过使用外推偏差法,得到索赔相依下的保险模型.通过最大化保险人和再保险人各自财富的加权,体现他们的共同利益.在模糊厌恶框架下,建立鲁棒随机优化问题.利用随机控制和随机动态规划理论求解鲁棒随机优化问题,得到鲁棒最优再保险和投资策略的显式解.最终,通过数值实验解释模型参数对鲁棒最优再保险和投资策略的影响,并指出研究结果的实际指导意义.Based on the expected utility maximization criterion,this paper studies the reinsurance and investment problem.There is an insurer and a reinsurer in the market.By using extrapolation deviation method,the insurance model under correlated claims is obtained.The joint interests of the insurer and the reinsurer are reflected by maximizing the weighted of their respective wealth.In the framework of ambiguity aversion,the robust stochastic optimization problem is established.By using stochastic control and stochastic dynamic programming theory to solve the robust stochastic optimization problem,the explicit solution of the robust optimal reinsurance and investment strategy is obtained.Finally,the effects of model parameters on the robust optimal reinsurance and investment strategy are explained by numerical experiments,and the practical guiding significance of the research results is pointed out.

关 键 词：鲁棒控制 索赔相依性 共同利益 再保险 投资 

分 类 号：O211.6[理学—概率论与数理统计] O225[理学—数学] F840[经济管理—保险]