On uniform tail expansions of multivariate copulas and wide convergence of measures. (English) Zbl 1102.62053

Jaworski, Piotr

Appl. Math. 33, No. 2, 159-184 (2006).

Summary: 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.

MSC:

62H05	Characterization and structure theory for multivariate probability distributions; copulas
62G32	Statistics of extreme values; tail inference
60B10	Convergence of probability measures
91B28	Finance etc. (MSC2000)
91B30	Risk theory, insurance (MSC2010)
28C10	Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
28A33	Spaces of measures, convergence of measures
60E05	Probability distributions: general theory

Keywords:

copulas; tails of probability distributions; dependence of extreme events; convergence of measures