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Decision Making Under Uncertainty When Preference Information Is Incomplete

Author

Listed:
  • Benjamin Armbruster

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

  • Erick Delage

    (Department of Decision Sciences, HEC Montréal, Montréal, Québec H3T 2A7, Canada)

Abstract

We consider the problem of optimal decision making under uncertainty but assume that the decision maker’s utility function is not completely known. Instead, we consider all the utilities that meet some criteria, such as preferring certain lotteries over other lotteries and being risk averse, S-shaped, or prudent. These criteria extend the ones used in the first- and second-order stochastic dominance framework. We then give tractable formulations for such decision-making problems. We formulate them as robust utility maximization problems, as optimization problems with stochastic dominance constraints, and as robust certainty equivalent maximization problems. We use a portfolio allocation problem to illustrate our results. This paper was accepted by Dimitris Bertsimas, optimization.

Suggested Citation

  • Benjamin Armbruster & Erick Delage, 2015. "Decision Making Under Uncertainty When Preference Information Is Incomplete," Management Science, INFORMS, vol. 61(1), pages 111-128, January.
    • Handle: RePEc:inm:ormnsc:v:61:y:2015:i:1:p:111-128
    DOI: 10.1287/mnsc.2014.2059
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    References listed on IDEAS

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    1. Meyer, Jack, 1977. "Choice among distributions," Journal of Economic Theory, Elsevier, vol. 14(2), pages 326-336, April.
    2. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    3. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    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. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    6. Aharon Ben‐Tal & Marc Teboulle, 2007. "An Old‐New Concept Of Convex Risk Measures: The Optimized Certainty Equivalent," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 449-476, July.
    7. Grable, John & Lytton, Ruth H., 1999. "Financial risk tolerance revisited: the development of a risk assessment instrument," Financial Services Review, Elsevier, vol. 8(3), pages 163-181.
    8. Juan Dubra & Fabio Maccheroni & Efe A. Ok, 2004. "Expected Utility Without the Completeness Axiom," Yale School of Management Working Papers ysm404, Yale School of Management.
    9. Hayne E. Leland, 1968. "Saving and Uncertainty: The Precautionary Demand for Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 82(3), pages 465-473.
    10. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
    11. Moshe Leshno & Haim Levy, 2002. "Preferred by "All" and Preferred by "Most" Decision Makers: Almost Stochastic Dominance," Management Science, INFORMS, vol. 48(8), pages 1074-1085, August.
    12. Dimitris Bertsimas & Allison O'Hair, 2013. "Learning Preferences Under Noise and Loss Aversion: An Optimization Approach," Operations Research, INFORMS, vol. 61(5), pages 1190-1199, October.
    13. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
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