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

Elena Di Bernardino, and Didier Rullière. "On an asymmetric extension of multivariate Archimedean copulas based on quadratic form." Dependence Modeling 4.1 (2016): 328-347, electronic only. <http://eudml.org/doc/287065>.

@article{ElenaDiBernardino2016,
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.},
author = {Elena Di Bernardino, Didier Rullière},
journal = {Dependence Modeling},
keywords = {Archimedean copulas; transformations of Archimedean copulas; quadratic form},
language = {eng},
number = {1},
pages = {328-347, electronic only},
title = {On an asymmetric extension of multivariate Archimedean copulas based on quadratic form},
url = {http://eudml.org/doc/287065},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Elena Di Bernardino
AU - Didier Rullière
TI - On an asymmetric extension of multivariate Archimedean copulas based on quadratic form
JO - Dependence Modeling
PY - 2016
VL - 4
IS - 1
SP - 328
EP - 347, electronic only
AB - 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.
LA - eng
KW - Archimedean copulas; transformations of Archimedean copulas; quadratic form
UR - http://eudml.org/doc/287065
ER -