数学科学学院学术报告[2024] 081号

(高水平大学建设系列报告961号)

报告题目: Optimal Claim-dependent Proportional Reinsurance under a Self-exciting Claim Model

报告人：张鑫 教授（东南大学）

报告时间：2024.08.16下午15:00-16:00pm

讲座地点：科技楼 514

报告内容：This talk investigates an optimal reinsurance problem for an insurance company with self-exciting claims, where the insurer's historical claims affect the claim intensity itself. We focus on a claim-dependent proportional reinsurance contact, where the term “claim-dependent" signifies that the insurer's risk retention ratio is allowed to depend on claim size. The insurer aims to maximize the expected utility of terminal wealth. By utilizing the dynamic programming principle and verification theorem, we obtain the optimal reinsurance strategy and corresponding value function in closed-form from the Hamilton-Jacobi-Bellman equation under an exponential utility function. We show that the claim-dependent proportional reinsurance is optimal among all types of reinsurance under the exponential utility maximization criterion. In addition, we present several analytical properties and numerical examples of the derived optimal strategy and provide economic insights through analytical and numerical analyses. In particular, we show the optimal claim-dependent proportional reinsurance can be considered as a continuous approximation of the step-wise risk sharing rule between the insurer and the reinsurer.

报告人简历：张鑫， 东南大学数学学院教授、博士生导师，主要从事金融保险中的随机控制与数据统计分析方面的研究，共主持国家自然科学基金青年基金1项，国家自然科学基金面上项目3项，教育部博士点专项基金(新教师类)  1项。在SIAM Journal on Control and Optimization、Insurance Mathematics and Economics、Applied Mathematics and Optimization、Quantitative Finance、Journal of Optimization Theory and Applications、Scandinavian Actuarial Journal等国内外期刊上发表论文三十余篇，先后访问过澳大利亚麦考瑞大学、英国利物浦大学、澳门大学、香港理工大学、加拿大约克大学，香港大学。

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　　　　　　　　　　　　　　　　 2024年8月14日