On a Discrete Markov-Modulated Risk Model with Random Premium Income and Delayed Claims

In this paper, a discrete Markov-modulated risk model with delayed claims, random premium income, and a constant dividend barrier is proposed. It is assumed that the random premium income and individual claims are affected by a Markov chain with finite state space. The model proposed is an extension of the discrete semi-Markov risk model with random premium income and delayed claims. Explicit expressions for the total expected discounted dividends until ruin are obtained by the method of generating function and the theory of difference equations. Finally, the effect of related parameters on the total expected discounted dividends are shown in several numerical examples