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Abstract
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The present paper considers a discrete-time risk model with a homogeneous, irreducible, and aperiodic Markov chain. The general distribution of total claim amounts is influenced by the environmental Markov chain and in the i-th period the
individual claim sizes are conditionally independent. We obtain the recursive formulae
for infinite time ruin probability using the technique of ordinary generating functions.
In addition, we give some restrictions which under those the ruin will not happen. In
the last part, we present some numerical illustrations for the results and give the prac-
tical problem through a fully developed case study in the domain of social insurance.
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