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

100%

Di Bernardino E., Rullière D.

Dependence Modeling

2016

tom 4

nr 1

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.

Some applications of the Archimedean copulas in the proof of the almost sure central limit theorem for ordinary maxima

88%

Dudziński M., Furmańczyk K.

Open Mathematics

2017

tom 15

nr 1

1024-1034

Our goal is to state and prove the almost sure central limit theorem for maxima (Mn) of X1, X2, ..., Xn, n ∈ ℕ, where (Xi) forms a stochastic process of identically distributed r.v.’s of the continuous type, such that, for any fixed n, the family of r.v.’s (X1, ...,Xn) has the Archimedean copula CΨ.

Ograniczanie wyników

1 Dependence Modeling

1 Open Mathematics

1 Di Bernardino E.

1 Dudziński M.

1 Furmańczyk K.

1 Rullière D.

1 2017

1 2016

Wyniki wyszukiwania

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

Some applications of the Archimedean copulas in the proof of the almost sure central limit theorem for ordinary maxima