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

Volume 33 / 2006

Piotr Jaworski Applicationes Mathematicae 33 (2006), 159-184 MSC: 62H05, 60E05, 60B10, 91B28, 91B30, 28C10, 28A33. DOI: 10.4064/am33-2-3

Abstract

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.

Authors

  • Piotr JaworskiInstitute of Mathematics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland
    e-mail

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