Exact expressions and upper bound for ruin probabilities in the compound Markov binomial model

The compound Markov binomial model was first proposed by Cossette et al. [Scandinavian Actuarial Journal (2003) 301] to introduce time-dependence in the aggregate claim amount increments. As pointed out in [Scandinavian Actuarial Journal (2003) 301], this model can be seen as an extension to Gerber’s compound binomial model. In this paper, we pursue the analysis of the compound Markov binomial model by first showing that the conditional infinite-time ruin probability is a compound geometric tail. Based on this property, an upper bound and asymptotic expression for ruin probabilities are then provided. Finally, special cases of claim amount distributions are considered which allow the exact calculation of ruin probabilities.