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Analysis of the Expected Shortfall of Aggregate Dependent Risks

Published online by Cambridge University Press:  17 April 2015

Stan Alink ,
Matthias Löwe  and
Mario V. Wüthrich
Stan Alink
Affiliation:
Katholieke Universiteit Nijmegen, Subfaculteit Wiskunde, Toernooiveld 1 – 6500 GL Nijmegen, The Netherlands
Matthias Löwe
Affiliation:
Westfälischen Wilhelms Universität Münster, Fachbereich Mathematik, Institut für Mathematische Statistik, Einsteinstrasse 62 – 48149 Münster, Germany
Mario V. Wüthrich
Affiliation:
Winterthur Insurance, Römerstrasse 17, P.O. Box 357, CH-8401 Winterthur, Switzerland
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Abstract

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We consider d identically and continuously distributed dependent risks X 1,…, Xd . Our main result is a theorem on the asymptotic behaviour of expected shortfall for the aggregate risks: there is a constant cd such that for large u we have . Moreover we study diversification effects in two dimensions, similar to our Value-at-Risk studies in [2].

Keywords

Archimedean copuladependent random variablesdiversification effectextreme value theoryexpected shortfallValue-at-Risk
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 35 , Issue 1 , May 2005 , pp. 25 - 43
Copyright
Copyright © ASTIN Bulletin 2005

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