Peaks-over-threshold stability of multivariate generalized Pareto distributions

Journal of Multivariate Analysis

Volumn 99, Issue 4, 2008, Pages 715-734

  Falk, Michael ^a   Guillou, Armelle ^b  

^a UNIVERSITY OF WÜRZBURG   (Germany)

^b UNIVERSITÉ DE STRASBOURG   (France)

Author keywords

Excess distribution; Expected shortfall; Linear portfolio; Multivariate extreme value distribution; Multivariate generalized Pareto distribution; Peaks over threshold stability

Indexed keywords

EID: 40749152780     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2007.03.009     Document Type: Article

References (25)

1. C. Acerbi, C. Sirtori, Expected shortfall as a tool for financial risk management, URL 〈http://www.gloriamundi.org/picsresources/ncs.pdf〉, 2001.
2. C. Acerbi, D. Tasche, Expected shortfall: a natural coherent alternative to value at risk, URL 〈http://www.gloriamundi.org/picsresources/expshortfall.pdf〉, 2001.
3. C. Acerbi, D. Tasche, On the coherence of expected shortfall, URL 〈http://www.gloriamundi.org/picsresources/cadt.pdf〉, 2002.
4. Balkema A.A., and de Haan L. Residual life time at great age. Ann. Probab. 2 (1974) 792-804
5. Beirlant J., Goegebeur Y., Segers J., Teugels J., De Waal D., and Ferro C. Statistics of Extremes: Theory and Applications (2004), Wiley, New York
6. Coles S. An Introduction to Statistical Modeling of Extreme Values, Springer Series in Statistics (2001), Springer, New York
7. M. Falk, On the excess distribution of sums of random variables in bivariate EV models, Revstat, 2007, in print.
8. Falk M., Hüsler J., and Reiss R.-D. Laws of Small Numbers: Extremes and Rare Events (1994), DMV Seminar, Birkhäuser, Basel
9. Falk M., Hüsler J., and Reiss R.-D. Laws of Small Numbers: Extremes and Rare Events. second ed. (2004), Birkhäuser, Basel
10. Falk M., and Michel R. Testing for tail independence in extreme value models. Ann. Inst. Statist. Math. 58 (2006) 261-290
11. Falk M., and Reiss R.-D. On Pickands coordinates in arbitrary dimensions. J. Multivariate Anal. 92 (2005) 426-453
12. Fougères A.-L. Multivariate extremes. In: Finkenstädt B., and Rootzén H. (Eds). Extreme Values in Finance, Telecommunications, and the Environment (2004), Chapman & Hall, Boca Raton, FL 373-388
13. Galambos J. The Asymptotic Theory of Extreme Order Statistics. second ed. (1987), Krieger, Malabar
14. de Haan L., and Resnick S.I. Limit theory for multivariate sample extremes. Z. Wahrsch. Verw. Gebiete 40 (1977) 317-337
15. Kaufmann E., and Reiss R.-D. Strong convergence of multivariate point processes of exceedances. Ann. Inst. Statist. Math. 45 (1993) 433-444
16. Kaufmann E., and Reiss R.-D. Approximation rates for multivariate exceedances. J. Statist. Plann. Inference 45 (1995) 235-245
17. Kotz S., and Nadarajah S. Extreme Value Distributions (2000), Imperial College Press, London
18. M. Macke, On the distribution of linear combinations of multivariate EVD and GPD distributed random vectors with an application to the expected shortfall of portfolios, Diploma Thesis, University of Würzburg, 2004, (in German).
19. R. Michel, Simulation and Estimation in Multivariate Generalized Pareto Models. Ph.D. Thesis, University of Würzburg, 2006.
20. Nadarajah S. Approximation for bivariate extreme values. Extremes 3 (2000) 87-98
21. Pickands III J. Statistical inference using extreme order statistics. Ann. Statist. 3 (1975) 119-131
22. J. Pickands III, Multivariate extreme value distributions, Proceedings of 43th Session ISI (Buenos Aires), 1981, pp. 859-878.
23. S.I. Resnick, Extreme Values, Regular Variation, and Point Processes, Applied Probabilities, vol. 4, Springer, New York, 1987.
24. Rootzén H., and Tajvidi N. Multivariate generalized Pareto distributions. Bernoulli 12 (2006) 917-930
25. N. Tajvidi, Characterization and some statistical aspects of univariate and multivariate generalised Pareto distributions, Ph.D. Thesis, Department of Mathematics, University of Göteborg, 1996.