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On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment

Published online by Cambridge University Press:  29 August 2014

Jean-Marie Reinhard
Jean-Marie Reinhard*
Affiliation:
Groupe AG, Brussels, Belgium
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Abstract

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We consider a risk model in which the claim inter-arrivals and amounts depend on a markovian environment process. Semi-Markov risk models are so introduced in a quite natural way. We derive some quantities of interest for the risk process and obtain a necessary and sufficient condition for the fairness of the risk (positive asymptotic non-ruin probabilities). These probabilities are explicitly calculated in a particular case (two possible states for the environment, exponential claim amounts distributions).

Keywords

Semi-Markov processesruin theory
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 14 , Issue 1 , April 1984 , pp. 23 - 43
Copyright
Copyright © International Actuarial Association 1984

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