Optimal Dividends under Model Uncertainty

TL;DR

This paper develops a model for optimal dividend distribution under uncertainty about the surplus process, characterizing the value function and optimal strategy through a non-linear HJB equation.

Contribution

It introduces a novel approach to dividend optimization considering model ambiguity, providing a unique solution and threshold strategy characterization.

Findings

The value function solves a non-linear Hamilton-Jacobi-Bellman variational inequality.

The optimal strategy is a threshold policy with smooth pasting conditions.

Continuity and monotonicity of the value function and threshold with respect to ambiguity parameter.

Abstract

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.