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Sharp Convex Bounds on the Aggregate Sums–An Alternative Proof

Listed author(s):
  • Chuancun Yin

    ()

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

  • Dan Zhu

    ()

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

Registered author(s):

    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.

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    Article provided by MDPI, Open Access Journal in its journal Risks.

    Volume (Year): 4 (2016)
    Issue (Month): 4 (September)
    Pages: 1-8

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    Handle: RePEc:gam:jrisks:v:4:y:2016:i:4:p:34-:d:79381
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    13. Kaas, R. & Dhaene, J. & Vyncke, D. & Goovaerts, M.J. & Denuit, M., 2002. "A Simple Geometric Proof that Comonotonic Risks Have the Convex-Largest Sum," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 32(01), pages 71-80, May.
    14. Mao, Tiantian & Hu, Taizhong, 2011. "A new proof of Cheung's characterization of comonotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 214-216, March.
    15. Bernard, Carole & Jiang, Xiao & Wang, Ruodu, 2014. "Risk aggregation with dependence uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 93-108.
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