Equilibrium reinsurance strategies for catastrophe and secondary claims under α-maxmin mean–variance criterion
研究了考虑巨灾索赔传染效应和二次索赔的再保险问题，采用α-最大最小均值方差准则处理模糊厌恶，通过扩展HJB方程求解时间不一致优化问题，发现巨灾再保险策略受二次索赔策略影响但反之不成立。
This paper investigates optimal reinsurance under the consideration of contagious catastrophe claims and secondary claims, and the intensity of the latter is modeled as a shot noise process impacted by the former. Also, an α -maxmin mean-variance (MV) criterion is adopted to allow the insurer to have different levels of ambiguity aversion attitudes, and the general mean-variance premium principle is applied to calculate the reinsurance premiums. To overcome the time-inconsistency issue in the problem, this paper solves the optimization problem via studying the corresponding Extended Hamilton–Jacobi–Bellman (EHJB) equation. With the help of some auxiliary problems, the existence and uniqueness of the optimal reinsurance strategies are demonstrated. Our research indicates that an insurer’s reinsurance strategy for catastrophe claims is influenced by the strategy for secondary claims, but not vice versa. Additionally, it is observed that, for catastrophe insurance businesses, the proportional reinsurance contract is optimal when applying variance premium principle, while the excess-of-loss reinsurance treaty is generally preferred under the expected value premium principle. Finally, the sensitivity analysis for optimal reinsurance strategies with respect to several model parameters are performed. • We investigate an optimal reinsurance design problem in continuous-time settings. • Contagion effects of catastrophic events are considered. • α -maxmin criterion is used under the mean-variance functional with penalty. • The reinsurance premium is assumed to be calculated using a generalized mean-variance principle. • Extended HJB equation is adopted to solve time-inconsistent stochastic optimization problem and determines the equilibrium reinsurance strategy.