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We shall find a multi-dimensional checkerboard copula of maximum entropy that matches an observed set of grade correlation coefficients. This problem is formulated as the maximization of a concave function on a convex polytope. • Under mild constraint qualifications we show that a unique solution exists in the core of the feasible region. • The theory of Fenchel duality is used to reformulate the problem as an unconstrained minimization which is well solved numerically using a Newton iteration.doi:10.3934/naco.2012.2.233 fatcat:lzieo7dcm5dxrcznyxjbiloy5u