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Document Details :

Title: On the Tail Behaviour of Sums of Dependent Risks
Author(s): BARBE, Philippe , FOUGÈRES, Anne-Laure , GENEST, Christian
Journal: ASTIN Bulletin
Volume: 36    Issue: 2   Date: 2006   
Pages: 361-373
DOI: 10.2143/AST.36.2.2017926

Abstract :
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.