ruin probabilities in a discrete-time risk process with homogeneous markov chain

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 practical problem through a fully developed case study in the domain of social insurance