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Bounds of general Fréchet classes. (English) Zbl 1251.60015
The manuscript deals with multivariate copulas with given margins. First, a characterization is given for all copulas belonging to a Fréchet class in terms of the \(n\)-increasing property and some simple bounds. Then a method is presented for interpreting the search of the bounds of a general Fréchet class in terms of a solution of a linear system of Diophantine equations. As a byproduct, some analytic constructions of bounds are presented.

60E05 Probability distributions: general theory
62H20 Measures of association (correlation, canonical correlation, etc.)
11D04 Linear Diophantine equations
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