Subject Classification: 62E20, 62H20, 62P05

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

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

We generalize the extreme value analysis for Archimedean copulas (see ALINK, LÖWE and WÜTHRICH, 2003) to the non-Archimedean case: Assume we have d ≥ 2 exchangeable and continuously distributed risks X 1 , . . ., X d . Under appropriate assumptions there is a constant q d such that, for all large u, we have PThe constant q d describes the asymptotic dependence structure. Typically, q d will depend on more aspects of this dependence structure than the well-known tail dependence coefficient.