Equilibrium Mean-Variance Dividend Rate Strategies

TL;DR

This paper develops a novel approach to optimal dividend strategies maximizing mean-variance objectives, addressing time inconsistency with a new verification method and identifying barrier strategies for low risk aversion.

Contribution

It introduces a verification lemma for time-inconsistent control problems and characterizes equilibrium dividend strategies in a stochastic setting.

Findings

Equilibrium strategies are barrier strategies for small risk aversion.

The verification lemma characterizes the value function and strategies.

The approach addresses the endogenous time horizon in dividend problems.

Abstract

This paper studies an optimal dividend problem for a company that aims to maximize the mean-variance (MV) objective of the accumulated discounted dividend payments up to its ruin time. The MV objective involves an integral form over a random horizon that depends endogenously on the company's dividend strategy, and these features lead to a novel time-inconsistent control problem. To address the time inconsistency, we seek a time-consistent equilibrium dividend rate strategy. We first develop and prove a new verification lemma that characterizes the value function and equilibrium strategy by an extended Hamilton-Jacobi-Bellman system. Next, we apply the verification lemma to obtain the equilibrium strategy and show that it is a barrier strategy for small levels of risk aversion.