Optimal Threshold Dividend Strategies under the Compound Poisson Model with Regime Switching

In this paper, we consider the optimal dividend strategy for an insurer whose surplus process is modeled by the classical compound Poisson risk model modulated by an observable continuous-time Markov chain. The object of the insurer is to select the dividend strategy that maximizes the expected total discounted dividend payments until ruin. We assume that the company only allows to pay dividend at a small rate. Given some conditions, similar to the results of Sotomayor and Cadenillas (2008) and Jiang and Pistorius (2008), the optimal strategy of our model is also a modulated threshold strategy which depends on the environment state. For the case of two regimes and exponential claim sizes, we obtain an analytical solution.