Optimal Dividend Policy when Cash Surplus Follows the Telegraph Process

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 a firm whose cash surplus exhibits regime switching, but unlike the existing literature, we exclude diffusion from our model. We assume that firm's cash surplus follows the telegraph process, which leads to a 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 by using the method of variational inequalities and show that the optimal dividend policy can be of three significantly different types depending on the parameters of the model.