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

Rob Kaas

出版	SSRN, 2006
URL	http://books.google.com.hk/books?id=7Q3tzgEACAAJ&hl=&source=gbs_api

註釋

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 + middot; middot; middot; + 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.