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Risks 2016, 4(4), 34; doi:10.3390/risks4040034

Sharp Convex Bounds on the Aggregate Sums–An Alternative Proof

School of Statistics, Qufu Normal University, Qufu 273165, Shandong, China
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Academic Editor: Mogens Steffensen
Received: 8 May 2016 / Revised: 17 September 2016 / Accepted: 21 September 2016 / Published: 29 September 2016
View Full-Text   |   Download PDF [323 KB, uploaded 29 September 2016]

Abstract

It is well known that a random vector with given marginals is comonotonic if and only if it has the largest convex sum, and that a random vector with given marginals (under an additional condition) is mutually exclusive if and only if it has the minimal convex sum. This paper provides an alternative proof of these two results using the theories of distortion risk measure and expected utility. View Full-Text
Keywords: comonotonicity; convex order; distortion risk measure; mutual exclusivity; stop-loss order comonotonicity; convex order; distortion risk measure; mutual exclusivity; stop-loss order
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Yin, C.; Zhu, D. Sharp Convex Bounds on the Aggregate Sums–An Alternative Proof. Risks 2016, 4, 34.

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