Stochastic Control of Dividends with a Drawdown Penalty

TL;DR

This paper studies an optimal dividend payout strategy in a diffusion risk model with a drawdown penalty, deriving explicit solutions and characterizing the optimal control policy.

Contribution

It introduces a novel model incorporating drawdown constraints into dividend optimization and explicitly solves for the optimal strategy and value function.

Findings

Optimal dividend rate is either zero or maximum u_0.

Explicit expression for the value function is derived.

Optimal strategy characterized by threshold-based control.

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.