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

摘要

The aim of this paper is to build recursive and integral equations for ruin probabilities of generalized risk processes under rates of interest with homogenous markov chain claims and homogenous markov chain premiums. Generalized Lundberg inequalities for ruin probabilities of these processes are derived by using recursive technique. We first give recursive equations for finite – time ruin probabilities 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 ruin probabilities and ultimate ruin probability in Theorem 3.1 and Theorem 3.2. These Theorems give upper bounds for finite – time ruin probabilities and ultimate ruin probability. A numerical example is given to illustrate results.