Kybernetika 51 no. 2, 212-230, 2015

Characterizations of Archimedean n-copulas

Włodzimierz WysockiDOI: 10.14736/kyb-2015-2-0212

Abstract:

We present three characterizations of $n$-dimensional Archimedean copulas: algebraic, differential and diagonal. The first is due to Jouini and Clemen. We formulate it in a more general form, in terms of an $n$-variable operation derived from a binary operation. The second characterization is in terms of first order partial derivatives of the copula. The last characterization uses diagonal generators, which are ``regular'' diagonal sections of copulas, enabling one to recover the copulas by means of an asymptotic representation.

Keywords:

Archimedean operation, additive generator, diagonal generator, multiplicative generator, (Archimedean) $n$-copula, (Archimedean) $n$-quasicopula

Classification:

62H20

paper.pdf

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