Tails of Copulas

The various copulas in the actuarial and statistical literature differ not so much in the degree of association they allow, but rather in which part of the distributions the association is strongest. In property and casualty applications there is interest in copulas that emphasize correlation among large losses, i.e., in the right tails of the distributions. Several copulas that have this characteristic are discussed. In addition, univariate functions of copulas are introduced that describe various aspects of the copulas, including tail concentration. Univariate descriptive functions can be thought of as an intermediate step between the several zero-dimensional measures of association (Kendall, Spearman, Gini, etc.) and the multi-dimensional copula function itself.

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