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A note on compound renewal risk models with dependence

par Cossette, Hélène;Larrivée-Hardy, Etienne;Marceau, Etienne;Trufin, Julien
Référence Journal of computational and applied mathematics, 285, page (295-311)
Publication Publié, 2015-09

Article révisé par les pairs

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Résumé :

Over the last decade, there have been a significant amount of research works on compoundrenewal risk models with dependence. These risk models assume a dependence relation betweeninterclaim times and claim amounts. In this paper, we pursue their investigation.Weapply change of measure techniques within the compound renewal risk models with dependenceto obtain exact expressions for the Gerber–Shiu discounted penalty function. Wepropose a more general approach than the usual one based on the random walk associatedto the risk process as it is presented in the literature. More refined, our method keeps theembedded information in the sequence of claim amounts and interclaim times and enablesus to derive an exact expression for the Gerber–Shiu discounted penalty function. Simulationis one of the advantages of change of measure techniques since we can find a new probabilitymeasure under which ruin occurs almost surely. In this paper, we investigate theimportance sampling method based on change of measure techniques to compute severalruin measures. Numerical illustrations are carried out for specific bivariate distributions ofthe interclaim time and the claim amount to approximate interesting ruin measures.