2021/09/19 by Prakash Chakraborty, Asaf Cohen, Chakraborty, Prakash +3 · 1 citation
Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #math.OC #math.PR
paper · pdf · doi:10.48550/arxiv.2109.09137
arxiv created 2021/09/19 · arxiv updated 2021/09/21
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 non-linear 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 non-linear and linear part at the location of the threshold. Furthermore, we obtain continuity and monotonicity of the value function and the threshold strategy with respect to the parameter that measures ambiguity of our model.