Probabilitiés De Ruine Pour Une Classe De Models De Risque Semi-Markoviens

We consider particular semi-Markov risk models M/SM and I~/SM for which the interarrival distributions are exponential with parameters depending of the risk type. We obtain theoretical expressions for the ruin probabilities on an infinite horizon. In the special case of exponential distributions for the claim amounts, rum probabilities are to both models solutions of linear differential systems. These systems are explicitly solved when there are only two risk types.