On some transformations of Archimedean copulas

On some transformations of Archimedean copulas

Thời gian: 09:00 đến 10:30 Ngày 10/08/2017

Địa điểm: B4-705, VIASM

Báo cáo viên: Didier

Tóm tắt:

In this presentation, we briefly recall some results on copulas, Archimedean copulas and tail dependence. We then discuss the impact of two classes of transformations on the multivariate tail dependence coefficients of some copulas. The considered transformations both act within the class of  Archimedean copulas and allow to build generators exhibiting any chosen tail dependence coefficients.

The first investigated class of transformations relies on functions composition. We focus on the case where the transformed copula exhibits some regular variation properties. We investigate the behaviour of these coefficients in cases that are close to tail independence. Some results are also given under specific conditions involving regularly varying hazard rates of components of the transformation.

The second investigated class of transformations is built in order to ensure the validity of the transformed Archimedean generator. We discuss properties of these transformations, and present some numerical illustrations showing that the transformation can improve both likelihood and tail dependence on a given data.

the talk is based on some joint works with Elena Di Bernardino (cnam, Paris).