## 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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### References:

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