Optimal periodic dividends with penalty payments under a diffusion model

Abstract

In this work, we examine the optimal periodic dividend problem with penalty payments for a diffusion model, where dividends are only paid at Poisson arrival times. Moreover, we assume that (observed) ruin or bankruptcy does not occur even if the surplus is negative, but the penalty payments happen. The goal is to seek an optimal periodic dividend strategy to maximize the expectation of the difference between the present value of dividends and penalty payments. We demonstrate that the optimal strategy is a periodic barrier strategy. For the exponential penalty function, the optimal periodic barrier and the explicit expression for the value function are determined. Several numerical instances are also presented.