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Finite - Time Ruin Probability for Sequences of Dependent Random Variables with Interest

The aim of this paper is to build an exact formula for ruin probability of generalized risk processes under interest force with assumption that claims and premiums are assumed to be positive-valued random variables and interests are assumed to be non - negative- valued random variables (claims, premiums and interests are assumed to be independent). In addition, they are homogeneous Markov chains. This situation is quite realistic for many situations. An exact formula for ruin (non-ruin) probabilities is derived in this paper.