Extreme VaR scenarios in higher dimensions

For a sequence of random variables X 1, ..., X n , the dependence scenario yielding the worst possible Value-at-Risk at a given level α for X 1+...+X n is known for n=2. In this paper we investigate this problem for higher dimensions. We provide a geometric interpretation highlighting the dependence structures which imply the worst possible scenario. For a portfolio (X 1,..., X n ) with given uniform marginals, we give an analytical solution sustaining the main result of Rüschendorf (Adv. Appl. Probab. 14(3):623-632, 1982). In general, our approach allows for numerical computation