Optimal risk exposure and dividend payout policies under model uncertainty

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.