In this paper, we consider an optimal robust reinsurance problem in a diffusion model for an ambiguity-averse insurer, who worries about ambiguity and aims to minimize the robust value involving the probability of absolute ruin and a penalization of model ambiguity. It is assumed that the insurer is allowed to purchase per-claim reinsurance to transfer its risk exposure, and that the reinsurance premium is computed according to the mean-variance premium principle which is a combination of the expected-value and variance premium principles. The optimal reinsurance strategy and the associated value function are derived explicitly by applying stochastic dynamic programming and by solving the corresponding boundary-value problem. We prove that there exists a unique point of inflection which relies on the penalty parameter greatly such that the robust value function is strictly concave up to the unique point of inflection and is strictly convex afterwards. It is also interesting to observe that the expression of the optimal robust reinsurance strategy is independent of the penalty parameter and coincides with the one in the benchmark case without ambiguity. Finally, some numerical examples are presented to illustrate the effect of ambiguity aversion on our optimal results.

在本文中，我们考虑了一种避免歧义的保险人的扩散模型中的最优鲁棒再保险问题，该公司担心歧义，其目的是使涉及绝对破产概率和模型歧义惩罚的鲁棒值最小化。假定允许保险人购买每项索赔的再保险以转移其风险敞口，并且再保险费是根据均值方差保费原理计算的，均值方差保费原理是预期价值和方差保费原理的组合。通过应用随机动态规划并解决相应的边值问题，可以明确得出最优再保险策略和相关的价值函数。我们证明存在一个极大地依赖惩罚参数的唯一拐点，从而鲁棒值函数直到唯一拐点为止都是严格凹的，之后才是严格凸的。有趣的是，最优鲁棒再保险策略的表达式与惩罚参数无关，并且与基准情况下的惩罚参数一致。最后，通过一些数值例子说明了歧义厌恶对我们最优结果的影响。有趣的是，最佳鲁棒再保险策略的表达与惩罚参数无关，并且与基准情况下的惩罚参数一致。最后，通过一些数值例子说明了歧义厌恶对我们最优结果的影响。有趣的是，最佳鲁棒再保险策略的表达与惩罚参数无关，并且与基准情况下的惩罚参数一致。最后，通过一些数值例子说明了歧义厌恶对我们最优结果的影响。