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.

中文翻译：

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[公式省略]-最大均值-方差标准下巨灾和二次索赔的均衡再保险策略


本文研究了在考虑传染性巨灾索赔和二次索赔的情况下的最佳再保险，后者的强度被建模为受前者影响的散粒噪声过程。此外，采用 α-maxmin 均值-方差 （MV） 标准，允许保险公司具有不同程度的歧义厌恶态度，并应用一般均值-方差保费原则来计算再保险费。为了克服问题中的时间不一致问题，该文通过研究相应的扩展 Hamilton-Jacobi-Bellman （EHJB） 方程来解决优化问题。在一些辅助问题的帮助下，证明了最佳再保险策略的存在性和独特性。我们的研究表明，保险公司的巨灾索赔再保险策略会受到二次索赔策略的影响，但反之则不然。此外，据观察，对于巨灾保险业务，适用差价保费原则时，比例再保险合同是最优的，而在预期价值保费原则下，超额损失再保险条约通常是首选。最后，对几个模型参数进行最佳再保险策略的敏感性分析。