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Sharp Convex Bounds on the Aggregate Sums–An Alternative Proof

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  • Chuancun Yin

    () (School of Statistics, Qufu Normal University, Qufu 273165, Shandong, China)

  • Dan Zhu

    () (School of Statistics, Qufu Normal University, Qufu 273165, Shandong, China)

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.

Suggested Citation

  • Chuancun Yin & Dan Zhu, 2016. "Sharp Convex Bounds on the Aggregate Sums–An Alternative Proof," Risks, MDPI, Open Access Journal, vol. 4(4), pages 1-8, September.
  • Handle: RePEc:gam:jrisks:v:4:y:2016:i:4:p:34-:d:79381
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    References listed on IDEAS

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    More about this item

    Keywords

    comonotonicity; convex order; distortion risk measure; mutual exclusivity; stop-loss order;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • G0 - Financial Economics - - General
    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • G3 - Financial Economics - - Corporate Finance and Governance
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics
    • M4 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting
    • K2 - Law and Economics - - Regulation and Business Law

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