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Optimization Under First Order Stochastic Dominance Constraints

Author

Listed:
  • 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.

Suggested Citation

  • 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.
  • Handle: RePEc:wpa:wuwpge:0403002
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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.
    2. 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.
    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. "Convexification of Stochastic Ordering," GE, Growth, Math methods 0402005, University Library of Munich, Germany, revised 05 Aug 2005.
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    Citations

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    Cited by:

    1. Dentcheva, Darinka & Ruszczynski, Andrzej, 2006. "Portfolio optimization with stochastic dominance constraints," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 433-451, February.
    2. repec:spr:annopr:v:260:y:2018:i:1:d:10.1007_s10479-016-2387-x is not listed on IDEAS
    3. Christian Tassak & Jules Sadefo Kamdem & Louis Aimé Fono, 2012. "Dominances on fuzzy variables based on credibility measure," Working Papers hal-00796215, HAL.
    4. X. J. Tong & H. Xu & F. F. Wu & Z. Zhao, 2016. "Penalized sample average approximation methods for stochastic programs in economic and secure dispatch of a power system," Computational Management Science, Springer, vol. 13(3), pages 393-422, July.
    5. repec:spr:joptap:v:155:y:2012:i:3:d:10.1007_s10957-012-0089-3 is not listed on IDEAS
    6. Jinwook Lee & András Prékopa, 2015. "Decision-making from a risk assessment perspective for Corporate Mergers and Acquisitions," Computational Management Science, Springer, vol. 12(2), pages 243-266, April.
    7. repec:pal:jorsoc:v:68:y:2017:i:12:d:10.1057_s41274-016-0164-5 is not listed on IDEAS
    8. Dentcheva Darinka & Stock Gregory J. & Rekeda Ludmyla, 2011. "Mean-risk tests of stochastic dominance," Statistics & Risk Modeling, De Gruyter, vol. 28(2), pages 97-118, May.
    9. repec:spr:annopr:v:236:y:2016:i:2:d:10.1007_s10479-013-1369-5 is not listed on IDEAS
    10. repec:spr:annopr:v:253:y:2017:i:1:d:10.1007_s10479-016-2299-9 is not listed on IDEAS
    11. Andrey Lizyayev, 2010. "Stochastic Dominance Efficiency Analysis of Diversified Portfolios: Classification, Comparison and Refinements," Tinbergen Institute Discussion Papers 10-084/2, Tinbergen Institute.
    12. Guo, Xu & Wong, Wing-Keung, 2016. "Multivariate Stochastic Dominance for Risk Averters and Risk Seekers," MPRA Paper 70637, University Library of Munich, Germany.
    13. Darinka Dentcheva & Andrzej Ruszczynski, 2004. "Convexification of Stochastic Ordering," GE, Growth, Math methods 0402005, University Library of Munich, Germany, revised 05 Aug 2005.
    14. repec:spr:joptap:v:152:y:2012:i:2:d:10.1007_s10957-011-9903-6 is not listed on IDEAS
    15. 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.
    16. repec:spr:annopr:v:259:y:2017:i:1:d:10.1007_s10479-017-2526-z is not listed on IDEAS
    17. 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.

    More about this item

    Keywords

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

    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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