Basic bounds of Fréchet classes
Kybernetika, Tome 50 (2014) no. 1, pp. 95-108.

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Algebraic bounds of Fréchet classes of copulas can be derived from the fundamental attributes of the associated copulas. A minimal system of algebraic bounds and related basic bounds can be defined using properties of pointed convex polyhedral cones and their relationship with non-negative solutions of systems of linear homogeneous Diophantine equations, largely studied in Combinatorics. The basic bounds are an algebraic improving of the Fréchet-Hoeffding bounds. We provide conditions of compatibility and propose tools for an explicit description of the basic bounds of simple Fréchet classes.
DOI : 10.14736/kyb-2014-1-0095
Classification : 11D75, 60E05, 62H20
Keywords: algebraic bound; basic bound; copula; Diophantine equation; Fréchet class; pointed convex polyhedral cone
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Skřivánek, Jaroslav. Basic bounds of Fréchet classes. Kybernetika, Tome 50 (2014) no. 1, pp. 95-108. doi : 10.14736/kyb-2014-1-0095. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-1-0095/

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