Thejani Gamage, USC

Abstract: The optimal dividend problem under the continuous time diffusion model with the dividend rate being restricted in a given interval is a standard problem in Stochastic Optimal Control. Unlike the standard literature, we shall particularly be interested in the case when the parameters of the model are not specified so that the optimal control cannot be explicitly determined. We therefore follow the recently developed method via the Reinforcement Learning (RL) to find the optimal strategy. Specifically, we shall design a corresponding RL-type entropy-regularized exploratory control problem, which randomizes the control actions, and balances the exploitation and exploration. We shall first carry out a theoretical analysis of the new relaxed control problem and then use a policy improvement argument, along with policy evaluation devices to construct approximating sequences of the optimal strategy. We present some numerical results using different parametrization families for the cost functional, to illustrate the effectiveness of the approximation schemes.