Risk measures related to the surplus process in the compound Markov binomial model

Gerber has proposed a compound binomial model, as an approximation to the classical risk model, to describe the surplus process of an insurance company. Within the compound binomial model, the claims occur according to a bionmial process with independent increments. Cossette et al. present a compound Markov binomial model which is an extension of Gerber’s model. The compound Markov binomial model is based on a Markov binomial process which introduces dependency between claim occurrences over time. In this paper, we study, in details, some properties of the surplus process within the compound Markov binomial model. Recursive formulas for the computation of the distribution of the severity of ruin and the surplus one period prior to ruin are provided. Finally, we examine the computation of the joint distribution of the surplus prior and after the ruin and the distribution of the claim causing ruin.