金融工程研究中心学术报告：Optimal risk sharing for two insurers in a mixed leadership game

报 告 人：梁志彬(南京师范大学) 报告时间：2024年11月18日 (周一) 上午10:00-11:00 报告地点：苏州大学览秀楼105 线上直播：腾讯会议 362-683-9628 报告摘要： In this paper, we investigate an optimal risk sharing problem for two insurers under the framework of mixed leadership game. More specifically, two insurers transfer their businesses to each other for achieving the goal of win-win where both of them act as the leader for pricing while the follower for choosing their own retention level. Under the criterion of maximizing the expected exponential utility of the terminal wealth, by solving the Hamilton-Jacobi-Bellman equations, the explicit optimal strategies are derived. In order to explore the advantages of risk sharing, we compare the results in two cases: with and without cooperation, and find that, when the two businesses are negatively correlated, both the insurers will definitely reach a win-win goal through cooperation. Besides, we also investigate the optimal reinsurance problem in a traditional leader-follower game framework, and find that risk sharing is more advantageous than reinsurance in many cases, especially when the businesses have significant differences, such as a strong negative correlation, or a large/small volatility ratio which means that one of the two businesses is relatively stable, while the other fluctuates greatly. Further analysis is given to show the effects of model parameters and the economics interpretations behind them. 报告人简介： 梁志彬，博士，南京师范大学数学科学学院教授，博士生导师。主要研究方向：风险管理与精算，数理金融与定价，随机最优风险控制。目前感兴趣的研究领域是：金融保险市场不确定环境下的博弈与优化；深度学习算法下的量化金融与随机最优控制。近年来，在SAJ，IME，EJOR，AMO等数理金融与精算以及优化相关期刊发表学术论文50余篇，主持和完成国家自然科学基金项目4项，省部级基金项目及横向项目多项。08年以来，先后访问过英国London Imperial College的Tanaka商学院；美国University of Michigan的数学系（先后三年半）；加拿大Concordia University的数学与统计系；美国北卡州立大学数学系；以及多次访问香港大学的统计与精算系等。