爱情岛论坛 学术报告[2026]099号

（高水平大学建设系列报告1358号）

报告题目：Optimal insurance design with persistent policyholder actions under a dynamic contagion claim process

报告人：孙中洋 教授 （曲阜师范大学）

报告时间：2026年10月23日9:30 - 10:30

报告地点：腾讯会议 384-532-834

报告摘要：This paper investigates the problem of optimal insurance design in a continuous-time setting. The claim arrival process is modeled by a dynamic contagion process that incorporates both self-exciting and externally excited jumps, thereby capturing the clustering of claims arising from the joint influence of endogenous factors and exogenous shocks. In the proposed model, the insurer offers a contract to a potential policyholder and specifies both the premium to be paid by the policyholder and the indemnity amount for each claim. In addition, the insurer may require the policyholder to undertake preventive actions that reduce the frequency of claims, which incur a cost to the policyholder. The insurer's objective is to maximize its expected total utility subject to a participation constraint, ensuring that the policyholder's expected utility from purchasing the contract is no less than that from not purchasing it. By applying the Lagrange multiplier method, we derive closed-form expressions for the optimal premium rate, the optimal indemnity per claim, and the policyholder's optimal action strategy. Finally, under exponential utility and a quadratic cost function, numerical experiments are carried out to illustrate how the optimal solutions respond to changes in key model parameters and to provide economic interpretations of the results.

报告人简介： 孙中洋，曲阜师范大学教授、博士生导师，山东省青年泰山学者。研究方向包括金融数学、保险与精算、随机最优控制等。主持国家自然科学基金面上项目和青年项目各1项、山东省自然科学基金等省部级项目4项。在《SIAM Journal on Control and Optimization》《Scandinavian Actuarial Journal》《Applied Mathematics and Optimization》《Journal of Optimization Theory and Applications》等期刊发表论文20余篇，出版学术专著1部。曾获山东省优秀研究生指导教师称号。

邀请人：李婧超

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