Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

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

On an asymmetric extension of multivariate Archimedean copulas based on quadratic form Abstract 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Dependence Modeling de Gruyter

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

Download PDF
20 pages

Loading next page...
 
/lp/de-gruyter/on-an-asymmetric-extension-of-multivariate-archimedean-copulas-based-QuqCtpcOfj
Publisher
de Gruyter
Copyright
Copyright © 2016 by the
ISSN
2300-2298
eISSN
2300-2298
DOI
10.1515/demo-2016-0019
Publisher site
See Article on Publisher Site

Abstract

Abstract 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.

Journal

Dependence Modeling – de Gruyter

Published: Dec 14, 2016

References

  • On the distortion of a copula and its margins
    Valdez
  • A new class of bivariate copulas
    Rodríguez
  • Transformations of copulas
    Klement
  • On the construction of copulas and quasi - copulas with given diagonal sections Insurance Math
    Nelsen
  • La fonction de dépendance empirique et ses propriétés
    Deheuvels
  • Hierarchical Kendall copulas : properties and inference
    Brechmann
  • Bivariate distributions with given extreme value attractor Multivariate
    Capéraà
  • Bivariate extreme statistics
    Sibuya
  • Sampling Archimedean copulas Data
    Hofert
  • Distortions of multivariate distribution functions and associated level curves : applications in multivariate risk theory Insurance Math
    Di Bernardino
  • Multivariate concordance Multivariate
    Joe
  • Sampling nested Archimedean copulas
    McNeil
  • Multivariate Archimax copulas Multivariate
    Charpentier
  • Construction of asymmetric multivariate copulas Multivariate
    Liebscher
  • New families of copulas based on periodic functions Statist Theory
    Alfonsi
  • Some new parametric families of multivariate copulas
    Dolati
  • Generalized bivariate copulas and their properties Model
    Kim
  • A method to obtain new copulas from a given one
    Morillas
  • Construction of asymmetric copulas and its application in two - dimensional reliability modelling European
    Wu
  • Nested Archimedean copulas meet R The nacopula package
    Hofert
  • From Archimedean to Liouville copulas Multivariate
    McNeil