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