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

Jean-Marie Reinhard

ASTIN Bulletin, 1984, vol. 14, issue 1, 23-43

Abstract: 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).

Date: 1984
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