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The complete mixability and convex minimization problems with monotone marginal densities

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  • Wang, Bin
  • Wang, Ruodu

Abstract

Following the results of Rüschendorf and Uckelmann (2002)Â [20], we introduce the completely mixable distributions on and prove that the distributions with monotone density and moderate mean are completely mixable. Using this method, we solve the minimization problem for convex functions f and marginal distributions P with monotone density. Our results also provide valuable implications in variance minimization, bounds for the sum of random variables and risk theory.

Suggested Citation

  • Wang, Bin & Wang, Ruodu, 2011. "The complete mixability and convex minimization problems with monotone marginal densities," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1344-1360, November.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:10:p:1344-1360
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    References listed on IDEAS

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    1. Yang, Jingping & Qi, Yongcheng & Wang, Ruodu, 2009. "A class of multivariate copulas with bivariate Frechet marginal copulas," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 139-147, August.
    2. Knott, Martin & Smith, Cyril, 2006. "Choosing joint distributions so that the variance of the sum is small," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1757-1765, September.
    3. Paul Embrechts & Giovanni Puccetti, 2006. "Bounds for Functions of Dependent Risks," Finance and Stochastics, Springer, vol. 10(3), pages 341-352, September.
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