Ruin Probability in a Generalized Risk Process under Interest Force with Homogenous Markov Chain Premiums

The aim of this paper is to give recursive and integral equations for ruin probabilities for generalized risk processes under interest force with homogenous markov chain premiums. Inequalities for ruin probabilities are derived by using recursive technique. We 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. These Theorems give upper bounds for finite-time probabilities and ultimate ruin probability.