On uniform tail expansions of multivariate copulas and wide convergence of measures

Piotr Jaworski¹

¹ Institute of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland

Applicationes Mathematicae, Tome 33 (2006) no. 2, pp. 159-184

Résumé

The theory of copulas provides a useful tool for modeling dependence in risk management. In insurance and finance, as well as in other applications, dependence of extreme events is particularly important, hence there is a need for a detailed study of the tail behaviour of multivariate copulas. We investigate the class of copulas having regular tails with a uniform expansion. We present several equivalent characterizations of uniform tail expansions. Next, basing on them, we determine the class of all possible leading parts of such expansions; we compute the leading parts of copulas popular in the literature, and discuss the statistical aspects of tail expansions.

Détail

DOI : 10.4064/am33-2-3

Keywords: theory copulas provides useful tool modeling dependence risk management insurance finance other applications dependence extreme events particularly important hence there detailed study tail behaviour multivariate copulas investigate class copulas having regular tails uniform expansion present several equivalent characterizations uniform tail expansions basing determine class possible leading parts expansions compute leading parts copulas popular literature discuss statistical aspects tail expansions