研究成果：Robust risk sharing and reinsurance contract design for contagious catastrophe and secondary claims under principal-agent framework
作者：冯杨
发表期刊：International Review of Financial Analysis；
期刊级别：ABS3
发表时间：2025年12月
摘要：This paper investigates the dynamic interaction between an insurer and a reinsurer in managing risks associated with primary catastrophe claims and descendant secondary claims under model uncertainty. To characterize the contagious nature of the catastrophic events, we model the aggregate catastrophe claims using a compound Poisson process and capture the aggregate secondary claims through a compound Cox process enhanced by a jump–diffusion Cox–Ingersoll–Ross (CIR) intensity. Specifically, we incorporate the size of catastrophe claims as the magnitude of positive externally-excited effect (i.e., contagious effect) driving the arrival intensity of secondary claims. Concerned with various ambiguities attributed from the reference models, the insurer and the reinsurer seek robust risk retention strategies and robust reinsurance premium pricing strategies, respectively, for both primary catastrophe claims and descendant secondary claims, aiming at maximizing their associated penalty-based mean–variance reward functions in the worst-case scenarios. To address the time-inconsistency issue inherent in the mean–variance criterion, we formulate the decision-making procedure as a non-cooperative game and provide an extended Hamilton–Jacobi–Bellman (HJB) equation in each robust optimization problem. Semi-analytical expressions for the unique robust equilibrium strategies and their corresponding value functions are derived under certain conditions. Numerical studies are conducted to discuss the economic implications of key parameters on robust equilibrium strategies in contagious catastrophic events and to analyze the sensitivity of utility losses arising from neglecting various ambiguities. These results not only indicate that both the insurer and the reinsurer tend to adopt conservative strategies under model uncertainty, but also reveal the interplay between the two parties in managing contagious catastrophe risks.