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/lp/de-gruyter/on-an-asymmetric-extension-of-multivariate-archimedean-copulas-based-020Znkf7Ul
- Publisher
- de Gruyter
- Copyright
- © 2016 Elena Di Bernardino and Didier Rullière
- ISSN
- 2300-2298
- eISSN
- 2300-2298
- DOI
- 10.1515/demo-2016-0019
- Publisher site
- See Article on Publisher Site
Abstract
AbstractAn important topic in Quantitative Risk Management concerns the modeling of dependence amongrisk 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 extensionsof the Archimedean copula family that make it possible to deal with asymmetry. Our extension is based onthe observation that when applied to the copula the inverse function of the generator of an Archimedeancopula can be expressed as a linear form of generator inverses. We propose to add a distortion term to thislinear part, which leads to asymmetric copulas. Parameters of this new class of copulas are grouped withina matrix, thus facilitating some usual applications as level curve determination or estimation. Some choicessuch as sub-model stability help associating each parameter to one bivariate projection of the copula. Wealso give some admissibility conditions for the considered copulas. We propose different examples as somenatural multivariate extensions of Farlie-Gumbel-Morgenstern or Gumbel-Barnett.
Journal
Dependence Modeling – de Gruyter
Published: Dec 14, 2016