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2014 | 2 | 1 |
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2014-09-12
zaakceptowano
2014-10-29
online
2014-11-10
Twórcy
  • Faculty of Economics and Management, Free University of Bozen-Bolzano, I-
    39100 Bolzano, Italy
  • Grupo de Investigación de Análisis Matemático, Universidad de Almería, La Cañada de San Urbano,
    Almería, Spain
  • Department for Mathematics, University of Salzburg, Salzburg, Austria
Bibliografia
  • [1] C. Alsina, A. Damas, and J. J. Quesada-Molina. Some functionals for copulas. Int. J. Math. Math. Sci., 14(1):45–54, 1991.
  • [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.
  • [3] B. De Baets, H. De Meyer, J. Kalická, and R. Mesiar. Flipping and cyclic shifting of binary aggregation functions. Fuzzy SetsSyst., 160(6):752–765, 2009.
  • [4] E. Di Bernardino and D. Rullière. On certain transformations of Archimedean copulas: Application to the non-parametricestimation of their generators. Dependence Modeling, 1:1–36, 2013.
  • [5] A. Dolati and M. Úbeda-Flores. Constructing copulas by means of pairs of order statistics. Kybernetika (Prague), 45(6):992–1002, 2009.
  • [6] F. Durante. A new class of symmetric bivariate copulas. J. Nonparametr. Stat., 18(7-8):499–510, (2007), 2006.
  • [7] F. Durante, J. Fernández-Sánchez, and R. Pappadà. Copulas, diagonals and tail dependence. Fuzzy Sets Syst., in press, 2015.
  • [8] F. Durante, J. Fernández-Sánchez, and C. Sempi. Multivariate patchwork copulas: a unified approach with applications topartial comonotonicity. Insurance Math. Econom., 53:897–905, 2013.
  • [9] F. Durante, R. Foschi, and P. Sarkoci. Distorted copulas: constructions and tail dependence. Comm. Statist. Theory Methods,39(12):2288–2301, 2010.
  • [10] F. Durante, A. Kolesárová, R. Mesiar, and C. Sempi. Semilinear copulas. Fuzzy Sets Syst., 159(1):63–76, 2008.
  • [11] C. Genest, J. J. Quesada-Molina, J. A. Rodríguez-Lallena, and C. Sempi. A characterization of quasi-copulas. J. MultivariateAnal., 69(2):193–205, 1999.
  • [12] E. P. Klement, R. Mesiar, and E. Pap. Transformations of copulas. Kybernetika (Prague), 41(4):425–434, 2005.
  • [13] A. Kolesárová and R. Mesiar. On linear and quadratic constructions of aggregation functions. Fuzzy Sets Syst., in press,2015.
  • [14] A. Kolesárová, R. Mesiar, and J. Kalická. On a new construction of 1–Lipschitz aggregation functions, quasi–copulas andcopulas. Fuzzy Sets Syst., 226:19–31, 2013.
  • [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.
  • [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.
  • [17] P. Mikusinski and M. D. Taylor. Some approximations of n-copulas. Metrika, 72(3):385–414, 2010.
  • [18] P. M. Morillas. A method to obtain new copulas from a given one. Metrika, 61(2):169–184, 2005.
  • [19] R. B. Nelsen. An introduction to copulas. Springer Series in Statistics. Springer, New York, second edition, 2006.
  • [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.
  • [21] P. Tankov. Improved Fréchet bounds and model-free pricing of multi-asset options. J. Appl. Probab., 48(2):389–403, 2011.
  • [22] E. A. Valdez and Y. Xiao. On the distortion of a copula and its margins. Scand. Actuar. J., 4:292–317, 2011.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_demo-2014-0005
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