Equilibrium Mean-Variance Dividend Rate Strategies

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.