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Peaks-over-threshold stability of multivariate generalized Pareto distributions

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  • Falk, Michael
  • Guillou, Armelle

Abstract

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

Suggested Citation

  • Falk, Michael & Guillou, Armelle, 2008. "Peaks-over-threshold stability of multivariate generalized Pareto distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 715-734, April.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:4:p:715-734
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    References listed on IDEAS

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    1. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    2. 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.
    3. Carlo Acerbi & Dirk Tasche, 2002. "Expected Shortfall: A Natural Coherent Alternative to Value at Risk," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 379-388, July.
    4. Falk, Michael & Reiss, Rolf-Dieter, 2005. "On Pickands coordinates in arbitrary dimensions," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 426-453, February.
    5. 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.
    6. 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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    Cited by:

    1. Indranil Ghosh & Osborne Banks, 2021. "A Study of Bivariate Generalized Pareto Distribution and its Dependence Structure Among Model Parameters," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 575-604, November.

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