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On an asymmetric extension of multivariate Archimedean copulas based on quadratic form

Elena Di Bernardino
  • Corresponding author
  • Elena Di Bernardino, CNAM, Paris, EA4629, Département IMATH, 292 rue Saint-Martin, Paris Cedex 03, France
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Didier Rullière
  • Corresponding author
  • Didier Rullière, Université de Lyon, Université Lyon 1, ISFA, Laboratoire SAF, 50 avenue Tony Garnier, 69366 Lyon, France
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2016-12-14 | DOI: https://doi.org/10.1515/demo-2016-0019


An important topic in Quantitative Risk Management concerns the modeling of dependence among risk sources and in this regard Archimedean copulas appear to be very useful. However, they exhibit symmetry, which is not always consistent with patterns observed in real world data. We investigate extensions of the Archimedean copula family that make it possible to deal with asymmetry. Our extension is based on the observation that when applied to the copula the inverse function of the generator of an Archimedean copula can be expressed as a linear form of generator inverses. We propose to add a distortion term to this linear part, which leads to asymmetric copulas. Parameters of this new class of copulas are grouped within a matrix, thus facilitating some usual applications as level curve determination or estimation. Some choices such as sub-model stability help associating each parameter to one bivariate projection of the copula. We also give some admissibility conditions for the considered copulas. We propose different examples as some natural multivariate extensions of Farlie-Gumbel-Morgenstern or Gumbel-Barnett.

Keywords: Archimedean copulas; transformations of Archimedean copulas; quadratic form


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About the article

Received: 2016-09-14

Accepted: 2016-11-15

Published Online: 2016-12-14

Citation Information: Dependence Modeling, Volume 4, Issue 1, ISSN (Online) 2300-2298, DOI: https://doi.org/10.1515/demo-2016-0019.

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© 2016 Elena Di Bernardino and Didier Rullière. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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