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Dependence Modeling

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Solution to an open problem about a transformation on the space of copulas

Fabrizio Durante
  • Faculty of Economics and Management, Free University of Bozen-Bolzano, I- 39100 Bolzano, Italy
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Juan Fernández-Sánchez
  • Grupo de Investigación de Análisis Matemático, Universidad de Almería, La Cañada de San Urbano, Almería, Spain
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Wolfgang Trutschnig
Published Online: 2014-11-10 | DOI: https://doi.org/10.2478/demo-2014-0005

Abstract

We solve a recent open problem about a new transformation mapping the set of copulas into itself. The obtained mapping is characterized in algebraic terms and some limit results are proved.

Keywords: Copula; Concordance; Quasi–copula

MSC: 62H05

References

  • [1] C. Alsina, A. Damas, and J. J. Quesada-Molina. Some functionals for copulas. Int. J. Math. Math. Sci., 14(1):45–54, 1991. CrossrefGoogle Scholar

  • [2] C. Bernard, X. Jiang, and S. Vanduffel. A note on “Improved Fréchet bounds and model-free pricing of multi-asset options” by Tankov (2011). J. Appl. Probab., 49(3):866–875, 2012. Google Scholar

  • [3] B. De Baets, H. De Meyer, J. Kalická, and R. Mesiar. Flipping and cyclic shifting of binary aggregation functions. Fuzzy Sets Syst., 160(6):752–765, 2009. Google Scholar

  • [4] E. Di Bernardino and D. Rullière. On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators. Dependence Modeling, 1:1–36, 2013. Google Scholar

  • [5] A. Dolati and M. Úbeda-Flores. Constructing copulas by means of pairs of order statistics. Kybernetika (Prague), 45(6):992– 1002, 2009. Google Scholar

  • [6] F. Durante. A new class of symmetric bivariate copulas. J. Nonparametr. Stat., 18(7-8):499–510, (2007), 2006. Google Scholar

  • [7] F. Durante, J. Fernández-Sánchez, and R. Pappadà. Copulas, diagonals and tail dependence. Fuzzy Sets Syst., in press, 2015. Web of ScienceGoogle Scholar

  • [8] F. Durante, J. Fernández-Sánchez, and C. Sempi. Multivariate patchwork copulas: a unified approach with applications to partial comonotonicity. Insurance Math. Econom., 53:897–905, 2013. Google Scholar

  • [9] F. Durante, R. Foschi, and P. Sarkoci. Distorted copulas: constructions and tail dependence. Comm. Statist. Theory Methods, 39(12):2288–2301, 2010. Web of ScienceGoogle Scholar

  • [10] F. Durante, A. Kolesárová, R. Mesiar, and C. Sempi. Semilinear copulas. Fuzzy Sets Syst., 159(1):63–76, 2008. Google Scholar

  • [11] C. Genest, J. J. Quesada-Molina, J. A. Rodríguez-Lallena, and C. Sempi. A characterization of quasi-copulas. J. Multivariate Anal., 69(2):193–205, 1999. Google Scholar

  • [12] E. P. Klement, R. Mesiar, and E. Pap. Transformations of copulas. Kybernetika (Prague), 41(4):425–434, 2005. Google Scholar

  • [13] A. Kolesárová and R. Mesiar. On linear and quadratic constructions of aggregation functions. Fuzzy Sets Syst., in press, 2015. Web of ScienceGoogle Scholar

  • [14] A. Kolesárová, R. Mesiar, and J. Kalická. On a new construction of 1–Lipschitz aggregation functions, quasi–copulas and copulas. Fuzzy Sets Syst., 226:19–31, 2013. Web of ScienceGoogle Scholar

  • [15] R. Mesiar and A. Stupnanová. Open problems from the 12th International Conference on Fuzzy Sets Theory and Its Applications. Fuzzy Sets Syst., in press, 2015. Web of ScienceGoogle Scholar

  • [16] F. Michiels and A. De Schepper. How to improve the fit of Archimedean copulas by means of transforms. Statist. Papers, 53(2):345–355, 2012. CrossrefGoogle Scholar

  • [17] P. Mikusinski and M. D. Taylor. Some approximations of n-copulas. Metrika, 72(3):385–414, 2010. Web of ScienceGoogle Scholar

  • [18] P. M. Morillas. A method to obtain new copulas from a given one. Metrika, 61(2):169–184, 2005. CrossrefGoogle Scholar

  • [19] R. B. Nelsen. An introduction to copulas. Springer Series in Statistics. Springer, New York, second edition, 2006. Google Scholar

  • [20] R. B. Nelsen and M. Úbeda-Flores. The lattice-theoretic structure of sets of bivariate copulas and quasi-copulas. C. R.Math. Acad. Sci. Paris, 341(9):583–586, 2005. Google Scholar

  • [21] P. Tankov. Improved Fréchet bounds and model-free pricing of multi-asset options. J. Appl. Probab., 48(2):389–403, 2011. Web of ScienceCrossrefGoogle Scholar

  • [22] E. A. Valdez and Y. Xiao. On the distortion of a copula and its margins. Scand. Actuar. J., 4:292–317, 2011.Web of ScienceCrossrefGoogle Scholar

About the article


Received: 2014-09-12

Accepted: 2014-10-29

Published Online: 2014-11-10


Citation Information: Dependence Modeling, Volume 2, Issue 1, ISSN (Online) 2300-2298, DOI: https://doi.org/10.2478/demo-2014-0005.

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© 2014 Fabrizio Durante et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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