We build a sharp approximation of the whole distribution of the sum of iid heavy-tailed random vectors, combining mean and extreme behaviors. It extends the so-called 'normex' approach from a univariate to a multivariate framework. We propose two possible multinormex distributions, named d-Normex and MRV-Normex. Both rely on the Gaussian distributi...
We analyze risk diversification in a portfolio of heavy-tailed risk factors under the assumption of second order multivariate regular variation. Asymptotic limits for a measure of diversification benefit are obtained when considering, for instance, the value-at-risk . The asymptotic limits are computed in a few examples exhibiting a variety of diff...
Published in Extremes
We survey the related asymptotic properties of multivariate distributions; (i) asymptotic independence, (ii) hidden regular variation, and (iii) multivariate second order regular variation. Connections and implications are discussed. The point of view of convergence of measures is emphasized in formulations because we are interested in the concepts...
