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Convexification of Stochastic Ordering

Author

Listed:
  • Darinka Dentcheva

    (Stevens Institute of Technology)

  • Andrzej Ruszczynski

    (Rutgers University)

Abstract

We consider sets defined by the usual stochastic ordering relation and by the second order stochastic dominance relation. Under fairy general assumptions we prove that in the space of integrable random variables the closed convex hull of the first set is equal to the second set.

Suggested Citation

  • Darinka Dentcheva & Andrzej Ruszczynski, 2004. "Convexification of Stochastic Ordering," GE, Growth, Math methods 0402005, University Library of Munich, Germany, revised 05 Aug 2005.
    • Handle: RePEc:wpa:wuwpge:0402005
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    References listed on IDEAS

    as
    1. Ronald E. Gangnon & William N. King, 2002. "Minimum distance estimation of the distribution functions of stochastically ordered random variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(4), pages 485-492, October.
    2. James P. Quirk & Rubin Saposnik, 1962. "Admissibility and Measurable Utility Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(2), pages 140-146.
    3. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    4. Darinka Dentcheva & Andrzej Ruszczynski, 2004. "Optimization Under First Order Stochastic Dominance Constraints," GE, Growth, Math methods 0403002, University Library of Munich, Germany, revised 07 Aug 2005.
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    Citations

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    Cited by:

    1. Darinka Dentcheva & Gabriela Martinez & Eli Wolfhagen, 2016. "Augmented Lagrangian Methods for Solving Optimization Problems with Stochastic-Order Constraints," Operations Research, INFORMS, vol. 64(6), pages 1451-1465, December.
    2. Darinka Dentcheva & Andrzej Ruszczynski, 2004. "Optimization Under First Order Stochastic Dominance Constraints," GE, Growth, Math methods 0403002, University Library of Munich, Germany, revised 07 Aug 2005.
    3. Pichler, Alois, 2013. "The natural Banach space for version independent risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 405-415.
    4. Dentcheva, Darinka & Ruszczynski, Andrzej, 2006. "Portfolio optimization with stochastic dominance constraints," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 433-451, February.
    5. Darinka Dentcheva & Andrzej Ruszczynski, 2005. "Inverse stochastic dominance constraints and rank dependent expected utility theory," GE, Growth, Math methods 0503001, University Library of Munich, Germany.
    6. Pflug Georg Ch., 2006. "On distortion functionals," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-16, July.

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    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D9 - Microeconomics - - Micro-Based Behavioral Economics

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