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

Author

Listed:
  • Durante Fabrizio

    (Faculty of Economics and Management, Free University of Bozen-Bolzano, I- 39100 Bolzano, Italy)

  • Fernández-Sánchez Juan

    (Grupo de Investigación de Análisis Matemático, Universidad de Almería, La Cañada de San Urbano, Almería, Spain)

  • Trutschnig Wolfgang

    (Department for Mathematics, University of Salzburg, Salzburg, Austria)

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.

Suggested Citation

  • Durante Fabrizio & Fernández-Sánchez Juan & Trutschnig Wolfgang, 2014. "Solution to an open problem about a transformation on the space of copulas," Dependence Modeling, De Gruyter, vol. 2(1), pages 1-8, November.
    • Handle: RePEc:vrs:demode:v:2:y:2014:i:1:p:8:n:5
    DOI: 10.2478/demo-2014-0005
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    References listed on IDEAS

    as
    1. Durante, Fabrizio & Fernández Sánchez, Juan & Sempi, Carlo, 2013. "Multivariate patchwork copulas: A unified approach with applications to partial comonotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 897-905.
    2. Di Bernardino Elena & Rullière Didier, 2013. "On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators," Dependence Modeling, De Gruyter, vol. 1(2013), pages 1-36, October.
    3. Piotr Mikusiński & Michael Taylor, 2010. "Some approximations of n-copulas," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(3), pages 385-414, November.
    4. repec:hal:wpaper:hal-00834000 is not listed on IDEAS
    5. Frederik Michiels & Ann De Schepper, 2012. "How to improve the fit of Archimedean copulas by means of transforms," Statistical Papers, Springer, vol. 53(2), pages 345-355, May.
    6. Peter Tankov, 2010. "Improved Frechet bounds and model-free pricing of multi-asset options," Papers 1004.4153, arXiv.org, revised Mar 2011.
    7. Valdez, Emiliano A., 2009. "On the Distortion of a Copula and its Margins," MPRA Paper 20524, University Library of Munich, Germany.
    8. Genest, C. & Quesada Molina, J. J. & Rodriguez Lallena, J. A. & Sempi, C., 1999. "A Characterization of Quasi-copulas," Journal of Multivariate Analysis, Elsevier, vol. 69(2), pages 193-205, May.
    9. Patricia Mariela Morillas, 2005. "A method to obtain new copulas from a given one," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(2), pages 169-184, April.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Boonmee Prakassawat & Tasena Santi, 2020. "Quadratic transformation of multivariate aggregation functions," Dependence Modeling, De Gruyter, vol. 8(1), pages 254-261, January.
    2. Boonmee Prakassawat & Tasena Santi, 2020. "Quadratic transformation of multivariate aggregation functions," Dependence Modeling, De Gruyter, vol. 8(1), pages 254-261, January.
    3. Girard Stéphane, 2018. "Transformation of a copula using the associated co-copula," Dependence Modeling, De Gruyter, vol. 6(1), pages 298-308, December.

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