A Simple Geometric Proof that Comonotonic Risks Have the Convex-Largest Sum
ASTIN Bulletin, Vol. 32, No. 1, pp. 71-80, 2002
12 Pages Posted: 2 Mar 2006
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.
Suggested Citation: Suggested Citation