This paper explores recursive and integral equations for ruin probability of a controlled risk process under rates of interest with homogenous Markov chains. We assume that claim and rates of interest are homogenous Markov chains, take a countable number of non – negative values. Generalized Lundberg inequalities for ruin probability of this process are derived via a recursive technique. Recursive equations for finite time ruin probability and an integral equation for ultimate ruin probability are presented, from which corresponding probability inequalities and upper bounds are obtained. An illustrative numerical example is discussed.
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