Characterizing Schur-concave commutative copulas as the closure of associative ones

Manuel Úbeda-Flores

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arXiv · 2605.02858

Characterizing Schur-concave commutative copulas as the closure of associative ones

Manuel Úbeda-Flores

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Abstract

Let $\mathcal{C}_a$ denote the class of associative copulas, and let $\overline{\mathcal{C}}_a$ be the closure, in the uniform metric $d_\infty$, of the convex hull of $\mathcal{C}_a$ . It is known that $\mathcal{C}_a \subseteq \mathcal{C}_{SC}$, the class of Schur-concave commutative copulas. We prove the reverse inclusion, establishing $\overline{\mathcal{C}}_a = \mathcal{C}_{SC}$.

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Manuel Úbeda-Flores. 2026-05-04. Characterizing Schur-concave commutative copulas as the closure of associative ones. https://arxiv.org/abs/2605.02858

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