Extreme VaR scenarios in higher dimensions |
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Authors: | Paul Embrechts Andrea Höing |
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Institution: | (1) Department of Mathematics, ETH Zürich, CH-8092 Zürich, Switzerland |
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Abstract: | 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 computations.
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Keywords: | Value-at-Risk Dependent risks Copulas |
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