Optimal Equilibrium Barrier Strategies for Time-Inconsistent Dividend Problems in Discrete Time

This paper studies a time-inconsistent dividend problem in discrete time with nonex- ponential discounting. Motivated by the decreasing impatience in behaviour economics, a general discount function is used and assumed to be log sub-additive. Using a game-theoretic approach equilibrium barrier strategies are considered. It is shown that in the case of multiple equilibria, there exists an optimal one that pointwisely dominates all the other equilibria. Case studies are conducted where there is no equilibrium, multiple equilibria, and a unique equilibrium