This paper investigates a combined optimal risk exposure and dividend distribution decision making problem in presence of model uncertainty. In the context of model uncertainty, the decision maker regards the reference model (fitted by observed information) as an approximation to the true model and believes that the true model exists in a family of alternative models surrounding the reference model. The aim is to find a robust strategy of risk exposure and dividend payments, which maximizes the expected cumulative discounted dividends until ruin plus a “penalty” on the distortion between the reference and alternative models in the worst-case scenario. We provide explicit expressions for the value functions and derive the respective optimal strategies explicitly. We show that the optimal dividend strategy is always of a barrier type and that it is optimal to retain full risk when the surplus is large. We also find that when the insurer is more averse to ambiguity, her optimal strategy on risk retention and dividend payout is more conservative.

本文研究了存在模型不确定性的最优风险敞口和股利分配决策的组合问题。在模型不确定性的情况下，决策者将参考模型（由观察到的信息拟合）视为真实模型的近似值，并认为真实模型存在于围绕参考模型的一系列替代模型中。目的是找到一个可靠的风险敞口和股息支付策略，该策略可以最大化预期的累积折现股息，直到破产为止，再加上在最坏情况下对参考模型和替代模型之间的失真的“惩罚”。我们为值函数提供了明确的表达式，并明确推导了各自的最优策略。我们表明，最优股利策略始终是障碍类型，当盈余很大时，保留全部风险是最优的。我们还发现，当保险公司不愿承担歧义时，她在风险保留和股利支付方面的最佳策略就更加保守。