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1 CEDRIC - Centre d-Etude et De Recherche en Informatique du Cnam 2 SAF - Laboratoire de Sciences Actuarielle et Financière

Abstract : This paper presents the impact of a class of transformations of copulas in their upper and lower multivariate tail dependence coefficients. In particular we focus on multivariate Archimedean copulas. In the first part of this paper, we calculate multivariate tail dependence coefficients when the generator of the considered copula exhibits some regular variation properties, and we investigate the behaviour of these coefficients in cases that are close to tail independence. This first part exploits previous works of Charpentier and Segers 2009 and extends some results of Juri and Wüthrich 2003 and De Luca and Rivieccio 2012. We also introduce a new Regular Index Function RIF exhibiting some interesting properties. In the second part of the paper we analyse the impact in the upper and lower multivariate tail dependence coefficients of a large class of transformations of dependence structures. These results are based on the transformations exploited by Di Bernardino and Rullière 2013. We extend some bivariate results of Durante et al. 2010 in a multivariate setting by calculating multivariate tail dependence coefficients for transformed copulas. We obtain new results under specific conditions involving regularly varying hazard rates of components of the transformation. In the third part, we show the utility of using transformed Archimedean copulas, as they permit to build Archimedean generators exhibiting any chosen couple of lower and upper tail dependence coefficients. The interest of such study is also illustrated through applications in bivariate settings. At last, we explain possible applications with Markov chains with specific dependence structure.

Keywords : regular variation tail dependence coefficients Archimedean copulas transformations of Archimedean copulas.

Author: Elena Di Bernardino - Didier Rullière -

Source: https://hal.archives-ouvertes.fr/


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