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.
copula, Fréchet class, Diophantine equation, algebraic bound, basic bound, pointed convex polyhedral cone
60E05, 62H20, 11D75