Higher-order expansions for compound distributions and ruin probabilities with subexponential claims

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Etat: Public
Version: de l'auteur⸱e
ID Serval
serval:BIB_69531DB42BB3
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
Higher-order expansions for compound distributions and ruin probabilities with subexponential claims
Périodique
Scandinavian Actuarial Journal
Auteur⸱e⸱s
Albrecher H., Hipp C., Kortschak D.
ISSN
0346-1238
Statut éditorial
Publié
Date de publication
2010
Peer-reviewed
Oui
Numéro
2
Pages
105-135
Langue
anglais
Résumé
Let X i (i=1,2, ...) be a sequence of subexponential positive independent and identically distributed random variables. In this paper, we offer two alternative approaches to obtain higher-order expansions of the tail of [image omitted] and subsequently for ruin probabilities in renewal risk models with claim sizes X i . In particular, these emphasize the importance of the term [image omitted] for the accuracy of the resulting asymptotic expansion of [image omitted] . Furthermore, we present a more rigorous approach to the often suggested technique of using approximations with shifted arguments. The cases of a Pareto type, Weibull and Lognormal distribution for X i are discussed in more detail and numerical investigations of the increase in accuracy by including higher-order terms in the approximation of ruin probabilities for finite realistic ranges of s are given.
Mots-clé
Asymptotic expansions, Subexponential distributions, Compound sums, Ruin theory
Web of science
Création de la notice
09/02/2009 18:43
Dernière modification de la notice
20/08/2019 14:24
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