Bivariate extension of the Pickands–Balkema–de Haan theorem

Mario V. Wüthrich

Annales de l'I.H.P. Probabilités et statistiques (2004)

  • Volume: 40, Issue: 1, page 33-41
  • ISSN: 0246-0203

How to cite

top

Wüthrich, Mario V.. "Bivariate extension of the Pickands–Balkema–de Haan theorem." Annales de l'I.H.P. Probabilités et statistiques 40.1 (2004): 33-41. <http://eudml.org/doc/77797>.

@article{Wüthrich2004,
author = {Wüthrich, Mario V.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Archimedean copula; dependent random variables; extreme value theory; Pickands-Balkema-de Haan theorem},
language = {eng},
number = {1},
pages = {33-41},
publisher = {Elsevier},
title = {Bivariate extension of the Pickands–Balkema–de Haan theorem},
url = {http://eudml.org/doc/77797},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Wüthrich, Mario V.
TI - Bivariate extension of the Pickands–Balkema–de Haan theorem
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2004
PB - Elsevier
VL - 40
IS - 1
SP - 33
EP - 41
LA - eng
KW - Archimedean copula; dependent random variables; extreme value theory; Pickands-Balkema-de Haan theorem
UR - http://eudml.org/doc/77797
ER -

References

top
  1. [1] A.A. Balkema, L. de Haan, Residual lifetime at great age, Ann. Probab.2 (1974) 792-804. Zbl0295.60014MR359049
  2. [2] P. Embrechts, C. Klüppelberg, T. Mikosch, Modelling Extremal Events for Insurance and Finance, Springer, Berlin, 1997. Zbl0873.62116MR1458613
  3. [3] P. Embrechts, A. McNeil, D. Straumann, Correlation and dependency in risk management: properties and pitfalls, in: Dempster M. (Ed.), Risk Management: Value at Risk and Beyond, Cambridge University Press, Cambridge, 2002, pp. 176-223. MR1892190
  4. [4] W.E. Frees, E.A. Valdez, Understanding relationships using copulas, North Amer. Actuarial J.2 (1998) 1-25. Zbl1081.62564MR1988432
  5. [5] C. Genest, J. MacKay, Copules archimediennes et familles de lois bidimensionelles dont les marges sont donnees, Canadian J. Statist.14 (1986) 154-159. Zbl0605.62049MR849869
  6. [6] C. Genest, J. MacKay, The joy of copulas: Bivariate distributions with uniform marginals, The American Statistican40 (1986) 280-283. MR866908
  7. [7] H. Joe, Multivariate Models and Dependence Concepts, Chapman & Hall, London, 1997. Zbl0990.62517MR1462613
  8. [8] A. Juri, M.V. Wüthrich, Copula convergence theorems for tail events, Insurance: Math. Econom.30 (3) (2002) 405-420. Zbl1039.62043MR1921115
  9. [9] A. Juri, M.V. Wüthrich, Tail dependence from a distributional point of view, Preprint, 2003. MR2081852
  10. [10] S. Kotz, S. Nadarajah, Extreme Value Distributions, Imperial College Press, London, 2000. Zbl0960.62051MR1892574
  11. [11] R.B. Nelsen, An Introduction to Copulas, Springer, New York, 1999. Zbl1152.62030MR1653203
  12. [12] J. Pickands, Statistical inference using extreme order statistics, Ann. Statist.3 (1975) 119-131. Zbl0312.62038MR423667
  13. [13] B. Schweizer, A. Sklar, Probabilistic Metric Spaces, North-Holland, New York, 1983. Zbl0546.60010MR790314
  14. [14] E. Senata, Regularly Varying Functions, Lecture Notes in Math., Springer, Heidelberg, 1976. Zbl0324.26002MR453936
  15. [15] A. Sklar, Fonctions de répartition à n dimensions et leurs marges, Publications de l'Institut de Statistique de l'Université de Paris8 (1959) 229-231. Zbl0100.14202MR125600
  16. [16] M.V. Wüthrich, Asymptotic value-at-risk estimates for sums of dependent random variables, Astin Bull.33 (1) (2003) 75-92. Zbl1098.62570MR1983861

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.