publication . Article . 2004

exact expressions and upper bound for ruin probabilities in the compound markov binomial model

Hélène Cossette; David Landriault; Étienne Marceau;
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  • Published: 11 May 2004 Journal: Insurance: Mathematics and Economics, volume 34, pages 449-466 (issn: 0167-6687, Copyright policy)
  • Publisher: Elsevier BV
Abstract
Abstract 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...
Subjects
free text keywords: Negative binomial distribution, Binomial approximation, Mathematics, Expression (mathematics), Binomial distribution, Markov chain, Binomial series, Upper and lower bounds, Ruin theory, Combinatorics
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