Insurance contracts pricing, that is determining the risk loading added to the expected loss, plays a fundamental role in insurance business. It covers the loss from adverse claim experience and generates a profit. As market competition is a key component in the pricing exercise, this paper proposes a novel dynamic pricing game model with multiple insurers who are competing with each other to sell insurance contracts by controlling their insurance premium. Different with the existing works assuming deterministic surplus/loss, we consider stochastic surplus and adopt the linear Brownian motion model, i.e., a diffusion approximation to the classical Cramér–Lundberg model, for the aggregate claim amount. The risk exposure of an insurer is assumed to be affected by all insurers in the market. By solving a system of Hamilton–Jacobi–Bellman (HJB) equations, Nash equilibrium premium strategies are explicitly obtained for the insurers who are aiming to maximize their expected terminal exponential utilities. The representation form of the equilibrium strategies relates to the so-called M-matrix, which appears in many economic models. To investigate the robustness of equilibrium pricing strategies under model uncertainty, we further extend the model by allowing insurers to perceive ambiguity towards the aggregate claim loss. Closed-form expression for the robust premium strategies are obtained and comparative statics are carried out for model parameters.

保险合同定价，即确定预期损失中增加的风险负担，在保险业务中起着根本作用。它弥补了不良索赔经历造成的损失并产生了利润。由于市场竞争是定价活动的关键组成部分，因此本文提出了一种新颖的动态定价博弈模型，该模型具有多个相互竞争以通过控制保险费来出售保险合同的保险人。与现有工作假设为确定性盈余/亏损的情况不同，我们考虑随机盈余并采用线性布朗运动模型，即对总索赔额的经典Cramér-Lundberg模型进行扩散近似。假定保险人的风险敞口受到市场上所有保险人的影响。通过解决汉密尔顿-雅各比-贝尔曼（HJB）方程组，可以明确为那些旨在最大化其预期最终指数效用的保险公司提供纳什均衡保费策略。均衡策略的表示形式与所谓的M-矩阵有关，它出现在许多经济模型中。为了研究模型不确定性下均衡定价策略的稳健性，我们通过允许保险公司感知总索赔损失的歧义来进一步扩展模型。获得了鲁棒保费策略的闭式表达式，并对模型参数进行了比较静力学。均衡策略的表示形式与所谓的M-矩阵有关，它出现在许多经济模型中。为了研究模型不确定性下均衡定价策略的稳健性，我们通过允许保险公司感知总索赔损失的歧义来进一步扩展模型。获得了鲁棒保费策略的闭式表达式，并对模型参数进行了比较静力学。均衡策略的表示形式与所谓的M-矩阵有关，它出现在许多经济模型中。为了研究模型不确定性下均衡定价策略的稳健性，我们通过允许保险公司感知总索赔损失的歧义来进一步扩展模型。获得了鲁棒保费策略的闭式表达式，并对模型参数进行了比较静力学。