Cossette, Hélène; Landriault, David; Marceau, Étienne Exact expressions and upper bound for ruin probabilities in the compound Markov binomial model. (English) Zbl 1188.91086 Insur. Math. Econ. 34, No. 3, 449-466 (2004). Summary: The compound Markov binomial model was first proposed by the authors [Scand. Actuar. J. 2003, No. 4, 301–323 (2003; Zbl 1092.91040)] 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. Cited in 15 Documents MSC: 91B30 Risk theory, insurance (MSC2010) 62P05 Applications of statistics to actuarial sciences and financial mathematics 60E05 Probability distributions: general theory 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 62E10 Characterization and structure theory of statistical distributions Keywords:ruin theory; compound Markov binomial model; dependence; compound binomial model; compound geometric tail; upper bound Citations:Zbl 1092.91040 PDFBibTeX XMLCite \textit{H. Cossette} et al., Insur. Math. Econ. 34, No. 3, 449--466 (2004; Zbl 1188.91086) Full Text: DOI References: [1] Cossette, H., Landriault, D., Marceau, E., 2003. Ruin probabilities in the compound Markov binomial model. Scandinavian Actuarial Journal, 301-323.; Cossette, H., Landriault, D., Marceau, E., 2003. 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