报告题目：Optimal risk allocation for an insurance group with reinsurance business
时 间：2024年12月12日（星期四）14：30
地 点：腾讯会议：（810-648-355 ）
主 办：数学与统计学院
参加对象：感兴趣的老师和学生
报告摘要：This talk is based on a paper that examines the optimal risk allocation problem for an insurance group composed of two companies, each considering the purchase of reinsurance to transfer their exposures. Specifically, the group’s manager determines how to allocate aggregate risks be- tween the two insurers to optimize total expected terminal wealth. Both entities can opt for excess-of-loss or proportional reinsurance based on the risks they assume to maximize their mean-variance preferences. For excess-of-loss reinsurance, we employ the calculus of variations to derive the necessary conditions for the optimal risk-sharing policy. Our findings indicate that the manager allocates all small-risk business to the insurer deemed more prof- itable. However, as risk increases, some business must inevitably be transferred to the other company. In the case of proportional reinsurance, we utilize convex analysis and step-by-step optimization methods to derive the optimal risk-sharing strategy. The results demonstrate that any admissible risk-sharing policy is dominated by either a change-loss or a dual change- loss form, contingent upon the coefficient of variation of the ceded loss. Finally, we present numerical examples to analyze the impact of various parameters on the optimal risk allocation strategies.
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。