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Aspects of optimization with stochastic dominance

Author

Listed:
  • William B. Haskell

    (National University of Singapore)

  • J. George Shanthikumar

    (Purdue University)

  • Z. Max Shen

    (University of California Berkeley)

Abstract

We consider stochastic optimization problems with integral stochastic order constraints. This problem class is characterized by an infinite number of constraints indexed by a function space of increasing concave utility functions. We are interested in effective numerical methods and a Lagrangian duality theory. First, we show how sample average approximation and linear programming can be combined to provide a computational scheme for this problem class. Then, we compute the Lagrangian dual problem to gain more insight into this problem class.

Suggested Citation

  • William B. Haskell & J. George Shanthikumar & Z. Max Shen, 2017. "Aspects of optimization with stochastic dominance," Annals of Operations Research, Springer, vol. 253(1), pages 247-273, June.
    • Handle: RePEc:spr:annopr:v:253:y:2017:i:1:d:10.1007_s10479-016-2299-9
    DOI: 10.1007/s10479-016-2299-9
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    References listed on IDEAS

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    1. Gebhard Geiger, 2012. "Multi-attribute non-expected utility," Annals of Operations Research, Springer, vol. 196(1), pages 263-292, July.
    2. Benjamin Armbruster & Erick Delage, 2015. "Decision Making Under Uncertainty When Preference Information Is Incomplete," Management Science, INFORMS, vol. 61(1), pages 111-128, January.
    3. Lizyayev, Andrey & Ruszczyński, Andrzej, 2012. "Tractable Almost Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 218(2), pages 448-455.
    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.
    5. Horst Zank, 2001. "Cumulative Prospect Theory for Parametric and Multiattribute Utilities," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 67-81, February.
    6. Ali E. Abbas, 2011. "Decomposing the Cross Derivatives of a Multiattribute Utility Function into Risk Attitude and Value," Decision Analysis, INFORMS, vol. 8(2), pages 103-116, June.
    7. Stoyan V. Stoyanov & Svetlozar T. Rachev & Frank J. Fabozzi, 2012. "Metrization Of Stochastic Dominance Rules," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-22.
    8. Ali E. Abbas, 2009. "Multiattribute Utility Copulas," Operations Research, INFORMS, vol. 57(6), pages 1367-1383, December.
    9. X. M. Hu & D. Ralph, 2004. "Convergence of a Penalty Method for Mathematical Programming with Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 365-390, November.
    10. Ralph L. Keeney, 1981. "Analysis of Preference Dependencies among Objectives," Operations Research, INFORMS, vol. 29(6), pages 1105-1120, December.
    11. Ilia Tsetlin & Robert L. Winkler, 2007. "Decision Making with Multiattribute Performance Targets: The Impact of Changes in Performance and Target Distributions," Operations Research, INFORMS, vol. 55(2), pages 226-233, April.
    12. David B. Brown & Melvyn Sim, 2009. "Satisficing Measures for Analysis of Risky Positions," Management Science, INFORMS, vol. 55(1), pages 71-84, January.
    13. Ali E. Abbas & Ronald A. Howard, 2005. "Attribute Dominance Utility," Decision Analysis, INFORMS, vol. 2(4), pages 185-206, December.
    14. Ralph L. Keeney, 1974. "Multiplicative Utility Functions," Operations Research, INFORMS, vol. 22(1), pages 22-34, February.
    15. Robert F. Bordley & Craig W. Kirkwood, 2004. "Multiattribute Preference Analysis with Performance Targets," Operations Research, INFORMS, vol. 52(6), pages 823-835, December.
    16. David B. Brown & Enrico De Giorgi & Melvyn Sim, 2012. "Aspirational Preferences and Their Representation by Risk Measures," Management Science, INFORMS, vol. 58(11), pages 2095-2113, November.
    17. William Haskell & J. Shanthikumar & Z. Shen, 2013. "Optimization with a class of multivariate integral stochastic order constraints," Annals of Operations Research, Springer, vol. 206(1), pages 147-162, July.
    18. Ali E. Abbas & Zhengwei Sun, 2015. "Multiattribute Utility Functions Satisfying Mutual Preferential Independence," Operations Research, INFORMS, vol. 63(2), pages 378-393, April.
    19. Manel Baucells & Rakesh K. Sarin, 2003. "Group Decisions with Multiple Criteria," Management Science, INFORMS, vol. 49(8), pages 1105-1118, August.
    20. Benjamin Armbruster & James Luedtke, 2015. "Models and formulations for multivariate dominance-constrained stochastic programs," IISE Transactions, Taylor & Francis Journals, vol. 47(1), pages 1-14, January.
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