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Copula convergence theorems for tail events. (English) Zbl 1039.62043
Summary: Tail dependence is studied from a distributional point of view by means of appropriate copulae. We derive similar results to the famous Pickands - Balkema - de Haan Theorem of Extreme Value Theory. Under regularity conditions, it is shown that the Clayton copula plays among the family of archimedean copulae the role of the generalized Pareto distribution. The practical usefulness of the results is illustrated in the analysis of stock market data.

MSC:
62G32 Statistics of extreme values; tail inference
62E20 Asymptotic distribution theory in statistics
62P05 Applications of statistics to actuarial sciences and financial mathematics
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