Multivariate Extremes and the Aggregation of Dependent Risks: Examples and counter-examples
by Paul Embrechts 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.
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.