On the Tail Behaviour of Sums of Dependent Risks

by Philippe Barbe Centre National de la Recherche Scientifique,
Anne-Laure Fougères of Équipe Modal'X & Université Paris X, and
Christian Genest of the Université Laval

November 2006

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.

Keywords: Archimedean copula, extremal behavior, multivariate regular variation, Pickands' representation.

Published in: ASTIN Bulletin, Vol. 36, No. 2, (November 2006), pp. 361-373.

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