Optimal Dividend Policy When Cash Surplus Follows Telegraph Process

Abstract

This article contributes to research dealing with the optimal dividend policy problem of a firm whose goal is to maximize the expected total discounted dividend payments before bankruptcy. We consider a model of firm whose cash surplus exhibits regime switching, but unlike the existing literature, we exclude diffusion from our model in order to over-come the well-known shortcoming of infinite money flows. Hence, we assume firm's cash surplus follows telegraph process, which leads to the problem of singular stochastic control. Surprisingly, this problem turns out to be more complicated than the ones arising in the models involving diffusion. We solve this problem using the method of variational inequalities and show that the optimal dividend policy is defined by two thresholds.