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Optimization Under First Order Stochastic Dominance Constraints

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Author Info

  • Darinka Dentcheva

    (Stevens Institute of Technology)

  • Andrzej Ruszczynski

    (Rutgers University)

Abstract

We consider stochastic optimization problems involving stochastic dominance constraints of first order, also called stochastic ordering constraints. They are equivalent to a continuum of probabilistic constraints or chance constraints. We develop first order necessary and sufficient conditions of optimality for these models. We show that the Lagrange multipliers corresponding to stochastic dominance constraints are piecewise constant nondecreasing utility functions. These results extend our theory of stochastic dominance-constrained optimization to the first order case, in which the main challenge is the potential non- convexity of the problem. We also show that the convexification of stochastic ordering relation is equivalent to second order stochastic dominance under rather weak assumptions. This paper appeared as "Semi-Infinite Probabilistic Optimization: First Order Stochastic Dominance Constraints" in "Optimization" 53(2004) 583-- 601.

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Bibliographic Info

Paper provided by EconWPA in its series GE, Growth, Math methods with number 0403002.

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Date of creation: 05 Mar 2004
Date of revision: 07 Aug 2005
Handle: RePEc:wpa:wuwpge:0403002

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Web page: http://128.118.178.162

Related research

Keywords: Stochastic dominance; stochastic ordering; stochastic programming; utility functions; semi-infinite optimization; optimality conditions; convexification.;

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References

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  1. Darinka Dentcheva & Andrzej Ruszczynski, 2004. "Convexification of Stochastic Ordering," GE, Growth, Math methods 0402005, EconWPA, revised 05 Aug 2005.
  2. 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.
  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. A. Charnes & W. W. Cooper & G. H. Symonds, 1958. "Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating Oil," Management Science, INFORMS, vol. 4(3), pages 235-263, April.
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Cited by:
  1. Andrey Lizyayev, 2010. "Stochastic Dominance Efficiency Analysis of Diversified Portfolios: Classification, Comparison and Refinements," Tinbergen Institute Discussion Papers 10-084/2, Tinbergen Institute.
  2. Christian Tassak & Jules SADEFO KAMDEM & Louis Aimé Fono, 2012. "Dominances on fuzzy variables based on credibility measure," Working Papers hal-00796215, HAL.
  3. Darinka Dentcheva & Andrzej Ruszczynski, 2005. "Inverse stochastic dominance constraints and rank dependent expected utility theory," GE, Growth, Math methods 0503001, EconWPA.
  4. Miguel Carrión & Uwe Gotzes & Rüdiger Schultz, 2009. "Risk aversion for an electricity retailer with second-order stochastic dominance constraints," Computational Management Science, Springer, vol. 6(2), pages 233-250, May.

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