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arXiv · 2512.12257

A complete characterization of maximal copulas with a given track section

Matjaž Omladič·Damjan Škulj
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Abstract

Bivariate copulas with prescribed diagonal section were first studied by Bertino. Their maximality was studied so far only from the point of view of upper bounds which brings quasi-copulas into the picture and limits the resulting set substantially. We propose to study maximality of these families in the order theoretic sense. A copula C with given diagonal section {\delta} is called undominated if there is no copula C' {\neq} C with the same diagonal section {\delta} such that C {\leq} C'. The main contribution of this paper is a new method that provides copulas of the kind. This method generates a much wider class that contains the known upper bounds as a very small subclass. There was a recent call for the study of asymmetry which is addressed by our class better than by the known ones. Corresponding quasi-copulas can be obtained from our copulas via splicing techniques. Most results are given on the level of tracks.

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Matjaž Omladič, Damjan Škulj. 2025-12-13. A complete characterization of maximal copulas with a given track section. https://arxiv.org/abs/2512.12257

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