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

Published online by Cambridge University Press:  29 August 2014

Jacques Janssen
Affiliation:
Université Libre de Bruxelles
Jean-Marie Reinhard
Affiliation:
Groupe AG
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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.

Type
Articles
Copyright
Copyright © International Actuarial Association 1985

References

Références

Gerber, H. U. (1979) An Introduction to Mathematical Risk Theory. Richard D. Irwin, Inc.: Homewood.Google Scholar
Janssen, J. (1982) Modèles de risque semi-markoviens. Cahiers du C.E.R.O. 24, 261280.Google Scholar
Reinhard, J. M. (1984) On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment. Astin Bulletin 14, 2343.CrossRefGoogle Scholar