This paper is devoted to investigating a non-zero-sum game between two competing insurers. The insurers can diversify their insurance risks by purchasing proportional reinsurance and investing their collected premiums into a financial market composed of one risk-free asset and one stock. The reinsurance premiums charged by the reinsurer follow the generalized mean–variance premium principle. Moreover, the dynamic CVaR constraints are incorporated in the game problem to control risks. With the dynamic mean–variance objective, we introduce two forward deterministic auxiliary processes to represent the expectations of the insurers’ wealth processes and transform the original time inconsistent game problem into a standard time consistent game problem with two state variables for each insurer. By adopting the dynamic programming principle and the Lagrange duality method, we derive the Nash equilibrium investment–reinsurance strategies for the two insurers. Finally, the effects of several important model parameters on the optimal policies are analyzed by numerical examples.

本文致力于研究两家相互竞争的保险公司之间的非零和博弈。保险公司可以通过购买比例再保险并将其收取的保费投资到由一种无风险资产和一种股票组成的金融市场来分散保险风险。再保险公司收取的再保险保费遵循广义均值方差保费原则。此外，动态CVaR约束被纳入博弈问题中以控制风险。利用动态均值方差目标，我们引入两个前向确定性辅助过程来表示保险公司财富过程的期望，并将原始时间不一致博弈问题转化为每个保险公司有两个状态变量的标准时间一致博弈问题。采用动态规划原理和拉格朗日对偶法，推导了两家保险公司的纳什均衡投资-再保险策略。最后，通过数值算例分析了几个重要模型参数对最优策略的影响。