Multivariate Extreme Value Theory And Its Usefulness In Understanding Risk

North American Actuarial Journal

Volumn 10, Issue 4, 2006, Pages 1-27

  Dupuis, Debbie J ^a   Jones, Bruce L ^b  

^a HEC MONTRÉAL   (Canada)

^b UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 61749096700     PISSN: 10920277     EISSN: None     Source Type: Journal    
DOI: 10.1080/10920277.2006.10597411     Document Type: Article

References (60)

1. Aarssen, Karin, and Laurens De Haan. 1994. On the Maximal Life Span of Humans. Mathematical Population Studies 4(4): 259-81.
2. Beirlant, Jan, Yuri Goegebeur, Johan Segers, and Jozef Teugels. 2004. Statistics of Extremes: Theory and Applications. Chichester: Wiley.
3. Belguise, Olivier, and Charles Levi. 2003. Tempêtes: Étude des dépendances entre les branches Automobile et Incendie à l’aide de la théorie des copules. 2003 ASTIN Colloquium, Berlin, Germany. www.astin2003.de/03 call 03.shtml.
4. Bouyé, Eric. 2002. Multivariate Extremes at Work for Portfolio Risk Measurement. Warwick Business School Working Paper Series, WP01-10.
5. Breymann, W. Alexandra Dias, and Paul Embrechts. 2003. Dependence Structures for Multivariate High-Frequency Data in Finance. Quantitative Finance 3: 1-14.
6. Capéraà, Philippe, Anne-Laure Fougères, and Christian Genest. 1997. A Nonparametric Estimation Procedure for Bivariate Extreme Value Copulas. Biometrika 84(3): 567-77.
7. Carriè Re, Jacques F. 1994. Dependent Decrement Theory. Transactions of the Society of Actuaries 46: 45-74.
8. Coles, Stuart. 2001. An Introduction to the Statistical Modeling of Extreme Values. London: Springer.
9. Coles, Stuart, Janet E. Heffernan, and Jonathan A. Tawn. 1999. Dependence Measures for Extreme Value Analyses. Extremes 2(4): 339-65.
10. Coles, Stuart G., and Jonathan A. Tawn. 1991. Modeling Extreme Multivariate Events. Journal of the Royal Statistical Society, Series B (Methodological) 53(2): 377-92.
11. Coles, Stuart G., and Jonathan A. Tawn. 1994. Statistical Methods for Multivariate Extremes: An Application to Structural Design (with discussion). Applied Statistics 43: 1-48.
12. Demarta, Stefano, and Alexander J. Mcneil. 2004. The t Copula and Related Copulas. Preprint available at www.math.ethz.ch/mcneil.
13. Denuit, Michel, Jan Dhaene, Marc Goovaerts, and Rob Kaas. 2005. Actuarial Theory for Dependent Risks. Chichester: Wiley.
14. Dupuis, Debbie J., and Jonathan A. Tawn. 2001. Effects of Mis-Specification in Bivariate Extreme Value Problems. Extremes 4(4): 315-30.
15. Embrechts, Paul, Claudia Klüppelberg, and Thomas Mikosch. 1997. Modeling Extremal Events for Insurance and Finance. Berlin: Springer.
16. Embrechts, Paul, Filip Lindskog, and Alexander Mcneil. 2003. Modeling Dependence with Copulas and Applications to Risk Management. In Handbook of Heavy Tailed Distributions in Finance, ed. S. T. Rachev, chap. 8, pp. 329-84. Amsterdam: Elsevier.
17. Embrechts, Paul, Sidney I. Resnick, and Gennady Samorodnitsky. 1999. Extreme Value Theory as a Risk Management Tool. North American Actuarial Journal 3(2): 30-41.
18. Fisher, R. A., and L. H. C. Tippett. 1928. Limiting Forms of the Frequency Distribution of the Largest or Smallest Member of a Sample. Proceedings of the Cambridge Philosophical Society 24: 180-90.
19. Frees, Edward W., Jacques F. Carrière, and Emiliano Valdez. 1996. Annuity Valuation with Dependent Mortality. Journal of Risk and Insurance 63: 229-61.
20. Frees, Edward W., and Emiliano A. Valdez. 1998. Understanding Relationships Using Copulas. North American Actuarial Journal 2(1): 1-25.
21. Gavrilov, Leonid A., and Natalia S. Gavrilova. 1991. The Biology of Life Span: A Quantitative Approach. Chur, Switzerland: Harwood Academic Publishers.
22. Geffroy, Jean. 1958-1959. Contributions à la théorie des valeurs extrêmes. Publications de l’Institut de Statistique de l’Université de Paris 7/8: 37-185.
23. Genest, Christian, Kilani Ghoudi, and Louis-Paul Rivest. 1998. Discussion of “Understanding Relationships Using Copulas” by Edward Frees and Emiliano Valdez. North American Actuarial Journal 2(3): 143-49.
24. Genest, Christian, and Louis-Paul Rivest. 1989. A Characterization of Gumbel’s Family of Extreme Value Distributions. Statistics and Probability Letters 8: 207-11.
25. Genest, Christian, and Louis-Paul Rivest. 1993. Statistical Inference Procedures for Bivariate Archimedean Copulas. Journal of the American Statistical Association 88: 1034-43.
26. Gumbel, E. J., and Neil Goldstein. 1964. Analysis of Empirical Bivariate Extremal Distributions. Journal of the American Statistical Association 59: 794-816.
27. Gumbel, E. J., and C. K. Mustafi. 1967. Some Analytical Properties of Bivariate Extremal Distributions. Journal of the American Statistical Association 62: 569-88.
28. De Haan, Laurens, and Sidney I. Resnick. 1993. Estimating the Limit Distribution of Multivariate Extremes. Communications in Statistics-Stochastic Models 9: 275-309.
29. De Haan, Laurens, and John De Ronde. 1998. Sea and Wind: Multivariate Extremes at Work. Extremes 1: 7-45.
30. Hall, Peter, and Nader Tajvidi. 2000. Distribution and Dependence Function Estimation for Bivariate Extreme-Value Distributions. Bernoulli 6: 835-44.
31. Heffernan, Janet E. 2000. A Directory of Coefficients of Tail Dependence. Extremes 3(3): 279-90.
32. Heffernan, Janet E., and Jonathan A. Tawn. 2004. A Conditional Approach for Multivariate Extreme Values. Journal of the Royal Statistical Society, Series B (Methodological), 66(2): 1-34.
33. Jenkinson, A. F. 1955. The Frequency Distribution of the Annual Maximum (or Minimum) of Meteorological Elements. Quarterly Journal of the Royal Meteorological Society 81: 158-71.
34. Joe, Harry. 1994. Multivariate Extreme-Value Distributions with Applications to Environmental Data. Canadian Journal of Statistics 22(1): 47-64.
35. Joe, Harry. 1997. Multivariate Models and Dependence Concepts. London: Chapman and Hall.
36. Joe, Harry, Richard L. Smith, and Ishay Weissman. 1992. Bivariate Threshold Methods for Extremes. Journal of the Royal Statistical Society, Series B (Methodological) 54: 171-83.
37. Juri, Alessandro, and Mario V. Wüthrich. 2002. Copula convergence Theorems for Tail Events. Insurance: Mathematics and Economics 30: 405-20.
38. Juri, Alessandro, and Mario V. Wüthrich. 2003. Tail Dependence from a Distributional Point of View. Extremes 6: 213-46.
39. Klugman, Stuart A., and Rahul Parsa. 1999. Fitting Bivariate Loss Distributions with Copulas. Insurance: Mathematics and Economics 24: 139-48.
40. Leadbetter, M. R., Georg Lindgren, and Holger Rootzén. 1983. Extremes and Related Properties of Random Sequences and Processes. Berlin: Springer.
41. Ledford, Anthony W., and Jonathan A. Tawn. 1996. Statistics for Near Independence in Multivariate Extreme Values. Biometrika 83(1): 169-87.
42. Ledford, Anthony W., and Jonathan A. Tawn. 1997. Modeling Dependence within Joint Tail Regions. Journal of the Royal Statistical Society, Series B (Methodological) 59(2): 475-99.
43. Ledford, Anthony W., and Jonathan A. Tawn. 1998. Concomitant Tail Behavior for Extemes. Advances in Applied Probability 30: 197-215.
44. Mardi, Kanti V. 1964. Asymptotic Independence of Bivariate Extremes. Calcutta Statistical Association Bulletin 13: 172-78.
45. Mcneil, Alexander J. 1997. Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory. ASTIN Bulletin 27(1): 117-37.
46. Nelsen, Roger B. 1999. An Introduction to Copulas. New York: Springer.
47. Peng, Liang. 1999. Estimation of the Coefficient of Tail Dependence in Bivariate Extremes. Statistics and Probability Letters 43: 399-409.
48. Pickands, James. 1975. Statistical Inference Using Extreme Order Statistics. Annals of Statistics 3(1): 119-31.
49. Pickands, James. 1981. Multivariate Extreme Value Distributions. Bulletin of the International Statistical Institute 49: 859-78.
50. Ramos, Alexandra, and Anthony Ledford. 2005. Regular Score Tests of Independence in Multivariate Extreme Values. Extremes 8(1-2): 5-26.
51. Resnick, Sidney I. 1987. Extreme Values, Regular Variation, and Point Processes. New York: Springer.
52. Rootzén, Holger, and Nader Tajvidi. 1997. Extreme Value Statistics and Wind Storm Losses: A Case Study. Scandinavian Actuarial Journal, 70-94.
53. Schmidt, Rafael, and Ulrich Stadtmüller. 2003. Nonparametric Estimation of Tail Dependence. London School of Economics, Department of Statistics, Research Report 101.
54. Shi, Daoji, Richard L. Smith, and Stuart G. Coles. 1992. Joint versus Marginal Estimation for Bivariate Extremes. Technical Report 2074. Department of Statistics, University of North Carolina, Chapel Hill.
55. Sibuya, Masaaki. 1960. Bivariate Extreme Statistics. Annals of the Institute of Statistical Mathematics 11: 195-210.
56. Tawn, Jonathan A. 1988. Bivariate Extreme Value Theory: Models and Estimation. Biometrika 75(3): 397-415.
57. Tiago De Oliveira, J. 1984. Bivariate Models for Extremes; Statistical Decision. In Statistical Extremes and Applications, ed. J. Tiago de Oliveira, pp. 131-53. Dordrecht: Reidel.
58. Venter, Gary G. 2002. Tails of Copulas. Proceedings of the Casualty Actuarial Society 89: 68-113.
59. Venter, Gary G. 2003. Fit to a t—Estimation, Application and Limitations of the t-Copula. 2003 ASTIN Colloquium, Berlin, Germany. www.astin2003.de/03 call 03.shtml.
60. Zhang, Zhengjun. 2006. A New Class of Tail-Dependent Time Series Models and Its Applications in Financial Time Series. Advances in Econometrics: Econometric Analysis of Financial and Economic Time Series Part B, 20, in Press.