Ruin Probabilities in the Compound Markov Binomial Model

Abstract

In this paper, we present a compound Markov binomial model which is an extension of the compound binomial model proposed by Gerber (1988a, b) and further examined by Shiu (1989) and Willmot (1993). The compound Markov binomial model is based on the Markov Bernoulli process which introduces dependency between claim occurrences. Recursive formulas are provided for the computation of the ruin probabilities over finite- and infinite-time horizons. A Lundberg exponential bound is derived for the ruin probability and numerical examples are also provided.

Keywords:

• Ruin theory
• Markov Bernoulli
• Markov binomial
• dependence
• compound binomial model
• Lundberg exponential bound
• recursive calculation

Acknowledgments

Partial funding in support of this work was provided by the Natural Sciences and Engineering Research Council of Canada, by the Fonds pour la formation de chercheurs et l'aide à la recherche (FCAR) du Gouvernement du Québec and by the Chaire en Assurance L'Industrielle-Alliance (Université Laval). The authors are grateful to an anonymous referee for his interesting comments which led to the improvement of the paper.