Stochastic Control of Dividends with a Drawdown Penalty

Abstract

We consider a diffusion risk model where dividends are paid at rate $U(t)\in [0,u_0]$. We are interested in maximising the dividend payments under a drawdown constraint, that is, we penalise a drawdown size larger than a level $d>0$. We show that the optimal dividend rate $U(t)$ is either zero or the maximal rate $u_0$ and determine the optimal strategy. Moreover, we derive an explicit expression for the value function by solving a system of differential equations.