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

Source abstract

Abstract In the recent actuarial literature, several proofs have been given for the fact that if a random vector ( X 1 X 2 , …, X n ) with given marginals has a comonotonic joint distribution, the sum X 1 + X 2 + … + X n 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.