Exploratory Dividend Optimization with Entropy Regularization

Abstract

This study investigates the dividend optimization problem in the entropy regularization framework in the continuous-time reinforcement learning setting. The exploratory HJB is established, and the optimal exploratory dividend policy is a truncated exponential distribution. We show that, for suitable choices of the maximal dividend-paying rate and the temperature parameter, the value function of the exploratory dividend optimization problem can be significantly different from the value function in the classical dividend optimization problem. In particular, the value function of the exploratory dividend optimization problem can be classified into three cases based on its monotonicity. Additionally, numerical examples are presented to show the effect of the temperature parameter on the solution. Our results suggest that insurance companies can adopt new exploratory dividend payout strategies in unknown market environments.