On the construction of copulas and quasi-copulas with given diagonal sections

Insurance: Mathematics and Economics

Volumn 42, Issue 2, 2008, Pages 473-483

  Nelsen, Roger B ^a   Quesada Molina, José Juan ^b   Rodríguez Lallena, José Antonio ^c   Úbeda Flores, Manuel ^c  

^a LEWIS AND CLARK COLLEGE   (United States)

^b UNIVERSITY OF GRANADA   (Spain)

^c UNIVERSITY OF ALMERÍA   (Spain)

Author keywords

Bounds; Copulas; Diagonal sections; Distribution functions; Quasi copulas

Indexed keywords

EID: 40949114627     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.insmatheco.2006.11.011     Document Type: Article

References (30)

1. Abdous B., Fougères A.-L., and Ghoudi K. Extreme behaviour for bivariate elliptical distributions. The Canadian Journal of Statistics 33 (2005) 317-334
2. Ané T., and Kharoubi C. Dependence structure and risk measure. Journal of Business 76 (2003) 411-438
3. Alsina C., Nelsen R.B., and Schweizer B. On the characterization of a class of binary operations on distribution functions. Statistics & Probability Letters 17 (1993) 85-89
4. Bäuerle N., and Müller A. Modelling and comparing dependencies in multivariate risk portfolios. Astin Bulletin 28 (1998) 59-67
5. Bertino S. Sulla dissomiglianza tra mutabili cicliche. Metron 35 (1977) 53-88
6. Denuit M., Dhaene J., Goovaerts M., and Kaas R. Actuarial Theory for Dependent Risk: Measures, Orders and Models (2005), John Wiley & Sons
7. Durante, F., Mesiar, R., Sempi, C., 2005. Copulas with given diagonal section: Some new results. In: Proceedings of EUSFLAT-LFA Conference. Barcelona, pp. 931-936
8. Durante F., Kolesárová A., Mesiar R., and Sempi C. Copulas with given diagonal sections: Novel constructions and applications. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15 (2007) 397-410
9. Embrechts P., McNeil A.J., and Straumann D. Correlation and dependence in risk management: Properties and pitfalls. Risk Management: Value at Risk and Beyond (2002), Cambridge University Press, Cambridge 176-223
10. Frahm G., Junker M., and Schmidt R. Estimating the tail dependence coefficient: Properties and pitfalls. Insurance: Mathematics and Economics 37 (2005) 80-100
11. Frahm G., Junker M., and Szimayer A. Elliptical copulas: Applicability and limitations. Statistics & Probability Letters 63 (2003) 275-286
12. Fredricks G.A., and Nelsen R.B. Copulas constructed from diagonal sections. Distributions with Given Marginals and Moment Problems (1997), Kluwer, Dordrecht 129-136
13. Fredricks G.A., and Nelsen R.B. The Bertino family of copulas. Distributions with Given Marginals and Statistical Modeling (2002), Kluwer, Dordrecht 81-92
14. Frees E.W., and Valdez E. Understanding relationships using copulas. North American Actuarial Journal 2 (1998) 1-25
15. Genest C., Quesada-Molina J.J., Rodríguez-Lallena J.A., and Sempi C. A characterization of quasi-copulas. Journal of Multivariate Analysis 69 (1999) 193-205
16. Joe H. Multivariate Models and Dependence Concepts (1997), Chapman & Hall, London
17. Klugman S.A., and Parsa R. Fitting bivariate loss distributions with copulas. Insurance: Mathematics and Economics 24 (1999) 139-148
18. Malevergne Y., and Sornette D. Extreme Financial Risks. From Dependence to Risk Management (2006), Springer-Verlag, Berlin
19. Mikusiński P., Sherwood H., and Taylor M.D. Shuffles of Min. Stochastica 13 (1992) 61-74
20. Nelsen R.B. An Introduction to Copulas. Second ed (2006), Springer, New York
21. Nelsen R.B., and Fredricks G.A. Diagonal copulas. Distributions with Given Marginals and Moment Problems (1997), Kluwer, Dordrecht 121-128
22. Nelsen R.B., Quesada-Molina J.J., and Rodríguez-Lallena J.A. Bivariate copulas with cubic sections. Journal of Nonparametric Statistics 7 (1997) 205-220
23. Nelsen R.B., Quesada-Molina J.J., Rodríguez-Lallena J.A., and Úbeda-Flores M. Distribution functions of copulas: A class of bivariate probability integral transforms. Statistics & Probability Letters 54 (2001) 277-282
24. Nelsen R.B., Quesada-Molina J.J., Rodríguez-Lallena J.A., and Úbeda-Flores M. Best-possible bounds on sets of bivariate distribution functions. Journal of Multivariate Analysis 90 (2004) 348-358
25. Nelsen R.B., Quesada-Molina J.J., Schweizer B., and Sempi C. Derivability of some operations on distribution functions. Distributions with Fixed Marginals and Related Topics. Lecture Notes-Monograph Series vol. 28 (1996), Institute of Mathematical Statistics, Hayward, CA 233-243
26. Nelsen R.B., and Úbeda-Flores M. The lattice-theoretic structure of sets of bivariate copulas and quasi-copulas. Comptes Rendus Mathématique 341 (2005) 583-586
27. Rodríguez-Lallena J.A., and Úbeda-Flores M. Best-possible bounds on sets of multivariate distribution functions. Communications in Statistics-Theory and Methods 33 (2004) 805-820
28. Schmidt R. Tail dependence for elliptically contoured distributions. Mathematical Methods of Operations Research 55 (2002) 301-327
29. Sklar A. Fonctions de répartition à n dimensions et leurs marges. Publications de l'Institut de Statistique de l'Université de Paris 8 (1959) 229-231
30. Úbeda-Flores, M., 2001. Cópulas y cuasicópulas: interrelaciones y nuevas propiedades. Aplicaciones (Ph.D. Dissertation). Servicio de Publicaciones de la Universidad de Almería, Spain