Properties of the compound Markov binomial model

Gerber (1988) has proposed a compound binomial model to describe the surplus process of an insurance company. This model was then studied by Shiu (1989), Willmot (1993) et Dickson (1994). Within the compound binomial model, the claims occur according to a binomial process with independent increments. Cossette et al. (2001) present a compound Markov binomial model which is an extension of the model proposed by Gerber (1988). The compound Markov binomial model is based on a Markov binomial process which introduces dependency between claim occurrences. In this paper, we study in detail the properties of the compound Markov binomial model. Recursive formulas for the computation of the distribution of the time of ruin are provided. We also examine the computation of the distribution of the surplus prior and after the ruin. Numerical examples are provided