Academic Report of School of Mathematical Sciences [2026] No. 099

(Series Report for High-Level University Construction No. 1358)

Title：Optimal insurance design with persistent policyholder actions under a dynamic contagion claim process

Speaker：Professor Sun Zhongyang (Qufu Normal University)

Time：9:30-10:30, Oct. 23, 2026

Location： Tencent Meeting: 384-532-834

Abstract: 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.

Speaker Profile： Sun Zhongyang is a professor and doctoral advisor at Qufu Normal University and a Shandong Provincial Young Taishan Scholar. His research interests include financial mathematics, insurance and actuarial science, and stochastic optimal control. He has led one General Program grant and one Young Scientist Program grant from the National Natural Science Foundation of China, as well as four provincial and ministerial-level projects, including grants from the Shandong Provincial Natural Science Foundation. He has published more than 20 papers in journals such as the SIAM Journal on Control and Optimization, the Scandinavian Actuarial Journal, Applied Mathematics and Optimization, and the Journal of Optimization Theory and Applications, and has authored one academic monograph. He was previously honored with the title of Outstanding Graduate Advisor in Shandong Province.

Faculty and students are welcome to attend!

Invited by: Li Jingchao

School of Mathematical Sciences

October 21, 2026