A simple geometric proof that comonotonic risks have the convex largest sum
(2002) Astin Bulletin : the journal of the International Actuarial Association — Vol. 32, n° 1, p. 71-80 (2002)
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- 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.
- Affiliations
Louvain School of Management
Citations
Kaas, R., Denuit, M., Goovaerts M., J., Vyncke, D., & Dhaene, J. (2002). A simple geometric proof that comonotonic risks have the convex largest sum. Astin Bulletin : the journal of the International Actuarial Association, 32(1), 71-80. https://doi.org/10.2143/AST.32.1.1015 (Original work published 2002)