Optimal Dividend Strategy for a General Diffusion Process with Time-Inconsistent Preferences and Ruin Penalty

This paper considers the optimal dividend strategy for a company whose cash holding follows a general diffusion process. The company's manager, who has time-inconsistent preferences, seeks the optimal dividend strategy and is subjected to a ruin penalty when the company goes bankrupt. We tackle the optimization problem by assuming that the manager is time-consistent, naïve, or sophisticated, and we obtain analytical solutions, respectively. Our results show that the sophisticated manager tends to pay out dividends earlier than the naïve manager, who in turn tends to pay out dividends earlier than the time-consistent manager, and that a manager with a higher level of time inconsistency tends to pay out dividends earlier; in contrast, the ruin penalty leads to delay in dividend payments. Finally, we provide several examples to illustrate our results.