Robust optimal dividend and reinsurance under model uncertainty

This paper considers the optimal dividend and reinsurance problem in presence of model uncertainty. The aim is to find a robust strategy of dividend and reinsurance to maximize the expected cumulative discounted dividend until ruin. Moreover, we penalize the expectation with an entropic term that accounts for the insurer's ambiguity concerning the risk model. By dynamic programming principle, we obtain the explicit optimal robust control strategy and the value function. Specially, the optimal strategy is to pay out any surplus immediately as dividends and then declare ruin when the insurer is highly averse enough to ambiguity. Finally, some numerical examples are presented to illustrate our results.