Ruin Probability in a Generalized Risk Process under Rates of Interest with Homogenous Markov Chain Claims

The aim of this paper is to give recursive and integral equations for ruin probabilities of generalized risk processes under interest force with homogenous Markov chain claims. Generalized Lundberg inequalities for ruin probabilities of these processes are derived by using recursive technique. We first give recursive equations for finite – time probability and an integral equation for ultimate ruin probability in Theorem 2.1 and Theorem 2.2. Using these equations, we can derive probability inequalities for finite – time probabilities and ultimate ruin probability in Theorem 3.1 and Theorem 3.2. The above results give upper bounds for finite – time probability and ultimate ruin probability.