Optimal dividend pay-outs in a regime switching model with bounded rate

In this note, we consider the optimal dividend payment strategy in regime-switching model under the bounded dividend rate restriction. The surplus of the insurance company is modelled as a regime switching Brownian motion, which has the drift and volatility from two-states Markov process control. The objective is to find the dividend policy which maximizes the expected total discounted dividend pay-outs until the time of bankruptcy. We derive the Hamilton-Jacobi-Bellman equation and closed form solution for the problem. Finally, a numerical simulation is presented to characterize the behavior of the optimal dividend payment strategy.