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Multivariate Extremes and the Aggregation of Dependent Risks: Examples and counter-examples

by Paul Embrechts of ETH Zurich,
Dominik D. Lambrigger of ETH Zurich, and
Mario V. WŁthrich of ETH Zurich

February 12, 2009

Abstract: Properties of risk measures for extreme risks have become an important topic of research. In the present paper we discuss sub- and superadditivity of quantile based risk measures and show how multivariate extreme value theory yields the ideal modeling environment. Numerous examples and counter-examples highlight the applicability of the main results obtained.

AMS Classification: 60G70, 62P05, 91B30, 62E20.

Keywords: multivariate extreme value theory, multivariate regular variation, risk aggregation, spectral measure, subadditivity, tail dependence, Value-at-Risk.

Published in: Extremes, Vol. 12, No. 2, (June, 2009), pp. 107-127.

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