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On the Tail Behavior of Sums of Dependent Risks

Published online by Cambridge University Press:  17 April 2015

Philippe Barbe ,
Anne-Laure Fougères  and
Christian Genest
Philippe Barbe
Affiliation:
Centre national de la recherche scientifique, 90, rue de Vaugirard, 75006 Paris, France
Anne-Laure Fougères
Affiliation:
Équipe Modal’X Unité de formation et de recherche SEGMI, Université Paris X – Nanterre, 200, avenue de la République, 92000 Nanterre, France
Christian Genest
Affiliation:
Département de mathématiques et de statistique, Université Laval, Québec (Québec), Canada G1K 7P4
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Abstract

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The tail behavior of sums of dependent risks was considered by Wüthrich (2003) and by Alink et al. (2004, 2005) in the case where the variables are exchangeable and connected through an Archimedean copula model. It is shown here how their result can be extended to a broader class of dependence structures using multivariate extreme-value theory. An explicit form is given for the asymptotic probability of extremal events, and the behavior of the latter is studied as a function of the indices of regular variation of both the copula and the common distribution of the risks.

Keywords

Archimedean copulaextremal behaviormultivariate regular variationPickands’ representation

Information

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 36 , Issue 2 , November 2006 , pp. 361 - 373
Copyright
Copyright © ASTIN Bulletin 2006

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