Optimal Dividends Under Model Uncertainty

We consider a diffusive model for optimally distributing dividends, while allowing for Knightian model ambiguity concerning the drift of the surplus process. We show that the value function is the unique solution of a nonlinear Hamilton-Jacobi-Bellman variational inequality. In addition, this value function embodies a unique optimal threshold strategy for the insurer's surplus, thereby making it the smooth pasting of a nonlinear and a linear part at the location of the threshold. Furthermore, we obtain continuity and monotonicity of the value function in addition to continuity of the threshold strategy with respect to the parameter that measures ambiguity of our model.