A Simple Geometric Proof that Comonotonic Risks Have the Convex-Largest Sum

Abstract In the recent actuarial literature, several proofs have been given for the fact that if a random vector (X1X2, …, Xn) with given marginals has a comonotonic joint distribution, the sum X1 + X2 + … + Xn is the largest possible in convex order. In this note we give a lucid proof of this fact, based on a geometric interpretation of the support of the comonotonic distribution.

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