Expected discounted dividends in a discrete semi-Markov risk model

In this paper, we consider the dividend problems for a discrete semi-Markov risk model, which assumes individual claims are influenced by a Markov chain with finite state space. Explicit expressions for the total expected discounted dividends until ruin are obtained in a case considered by Reinhard and Snoussi (2001, 2002). Then a more general situation is examined, in which a new method is developed to derive closed-form expressions for the total expected discounted dividends. For illustration purposes, only two-state and three-state models are examined. Finally, a numerical example is presented, which shows that the results obtained through different methods are equivalent.