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Document Details :

Title: A Simple Geometric Proof that Comonotonic Risks have the Convex-largest Sum
Author(s): KAAS, R. , DHAENE, J. , VYNCKE, D. , GOOVAERTS, M.J. , DENUIT, M.
Journal: ASTIN Bulletin
Volume: 32    Issue: 1   Date: May 2002   
Pages: 71-80
DOI: 10.2143/AST.32.1.1015

Abstract :
In the recent actuarial literature, several proofs have been given for the fact that if a random vector (X1, X2, …, 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.