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

See all articles by Rob Kaas

Rob Kaas

University of Amsterdam - Faculty of Economics & Econometrics (FEE)

Jan Dhaene

Katholieke Universiteit Leuven

David Vyncke

Ghent University - Department of Applied Mathematics and Computer Science

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics

Michel Denuit

Catholic University of Louvain

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.

Suggested Citation

Kaas, Rob and Dhaene, Jan and Vyncke, David and Goovaerts, Marc and Denuit, Michel, A Simple Geometric Proof that Comonotonic Risks Have the Convex-Largest Sum. ASTIN Bulletin, Vol. 32, No. 1, pp. 71-80, 2002, Available at SSRN: https://ssrn.com/abstract=886310

Rob Kaas (Contact Author)

University of Amsterdam - Faculty of Economics & Econometrics (FEE) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

Jan Dhaene

Katholieke Universiteit Leuven ( email )

Naamsestraat 69
Leuven, 3000
Belgium

David Vyncke

Ghent University - Department of Applied Mathematics and Computer Science ( email )

Gent, 9000
Belgium

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics ( email )

Leuven, B-3000
Belgium
+32 0 16 32 7446 (Phone)
+32 0 16 32 3740 (Fax)

Michel Denuit

Catholic University of Louvain ( email )

Place Montesquieu, 3
B-1348 Louvain-la-Neuve, 1348
Belgium

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