Peaks-over-threshold stability of multivariate generalized Pareto distributions
It is well-known that the univariate generalized Pareto distributions (GPD) are characterized by their peaks-over-threshold (POT) stability. We extend this result to multivariate GPDs. It is also shown that this POT stability is asymptotically shared by distributions which are in a certain neighborhood of a multivariate GPD. A multivariate extreme value distribution is a typical example. The usefulness of the results is demonstrated by various applications. We immediately obtain, for example, that the excess distribution of a linear portfolio with positive weights ai, i
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Volume (Year): 99 (2008)
Issue (Month): 4 (April)
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References listed on IDEAS
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- Carlo Acerbi & Dirk Tasche, 2001.
"On the coherence of Expected Shortfall,"
cond-mat/0104295, arXiv.org, revised May 2002.
- Carlo Acerbi & Dirk Tasche, 2001. "Expected Shortfall: a natural coherent alternative to Value at Risk," Papers cond-mat/0105191, arXiv.org.
- Falk, Michael & Reiss, Rolf-Dieter, 2005. "On Pickands coordinates in arbitrary dimensions," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 426-453, February.
- Michael Falk & René Michel, 2006. "Testing for Tail Independence in Extreme Value models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 261-290, June.
- E. Kaufmann & R. Reiss, 1993. "Strong convergence of multivariate point processes of exceedances," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 433-444, September.
- Carlo Acerbi & Claudio Nordio & Carlo Sirtori, 2001. "Expected Shortfall as a Tool for Financial Risk Management," Papers cond-mat/0102304, arXiv.org.
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