On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment
- 1 April 1984
- journal article
- Published by Cambridge University Press (CUP) in ASTIN Bulletin
- Vol. 14 (1), 23-43
- https://doi.org/10.1017/s0515036100004785
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).Keywords
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