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A simple geometric proof that comonotonic risks have the convex-largest sum. (English) Zbl 1061.62511

In the recent actuarial literature, several proofs have been given for the fact that if a random vector \((X_1,X_2,\dots, X_n)\) with given marginals has a comonotonic joint distribution, the sum \(X_1+ X_2+\cdots+ X_n\) 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.

MSC:

62E10 Characterization and structure theory of statistical distributions
60E15 Inequalities; stochastic orderings
62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
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