Probabilités de Ruine pour une Classe de Modèles de Risque Semi-Markoviens

Jacques Janssen; Jean-Marie Reinhard

doi:10.2143/AST.15.2.2015023

Abstract

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We consider particular semi-Markov risk models M/SM and /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, ruin probabilities are in both models solutions of linear differential systems. These systems are explicitly solved when there are only two risk types.

References

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Reinhard, J. M. (1984) On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment. Astin Bulletin 14, 23–43.CrossRef Google Scholar

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Probabilités de Ruine pour une Classe de Modèles de Risque Semi-Markoviens

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