On uniform tail expansions of multivariate copulas and wide convergence of measures
Tom 33 / 2006
Applicationes Mathematicae 33 (2006), 159-184
MSC: 62H05, 60E05, 60B10, 91B28, 91B30, 28C10, 28A33.
DOI: 10.4064/am33-2-3
Streszczenie
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.
