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Robust decision making over a set of random targets or risk-averse utilities with an application to portfolio optimization

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  • Jian Hu
  • Sanjay Mehrotra

Abstract

In many situations, decision-makers need to exceed a random target or make decisions using expected utilities. These two situations are equivalent when a decision-maker’s utility function is increasing and bounded. This article focuses on the problem where the random target has a concave cumulative distribution function (cdf) or a risk-averse decision-maker’s utility is concave (alternatively, the probability density function (pdf) of the random target or the decision-maker’ marginal utility is decreasing) and the concave cdf or utility can only be specified by an uncertainty set. Specifically, a robust (maximin) framework is studied to facilitate decision making in such situations. Functional bounds on the random target’s cdf and pdf are used. Additional general auxiliary requirements may also be used to describe the uncertainty set. It is shown that a discretized version of the problem may be formulated as a linear program. A result showing the convergence of discretized models for uncertainty sets specified using continuous functions is also proved. A portfolio investment decision problem is used to illustrate the construction and usefulness of the proposed decision-making framework.

Suggested Citation

  • Jian Hu & Sanjay Mehrotra, 2015. "Robust decision making over a set of random targets or risk-averse utilities with an application to portfolio optimization," IISE Transactions, Taylor & Francis Journals, vol. 47(4), pages 358-372, April.
    • Handle: RePEc:taf:uiiexx:v:47:y:2015:i:4:p:358-372
    DOI: 10.1080/0740817X.2014.919045
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    Citations

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    Cited by:

    1. Wei Wang & Huifu Xu, 2023. "Preference robust distortion risk measure and its application," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 389-434, April.
    2. Hu, Jian & Bansal, Manish & Mehrotra, Sanjay, 2018. "Robust decision making using a general utility set," European Journal of Operational Research, Elsevier, vol. 269(2), pages 699-714.
    3. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    4. Jian Hu & Junxuan Li & Sanjay Mehrotra, 2019. "A Data-Driven Functionally Robust Approach for Simultaneous Pricing and Order Quantity Decisions with Unknown Demand Function," Operations Research, INFORMS, vol. 67(6), pages 1564-1585, November.
    5. Jerry Anunrojwong & Krishnamurthy Iyer & David Lingenbrink, 2024. "Persuading Risk-Conscious Agents: A Geometric Approach," Operations Research, INFORMS, vol. 72(1), pages 151-166, January.
    6. William B. Haskell & Wenjie Huang & Huifu Xu, 2018. "Preference Elicitation and Robust Optimization with Multi-Attribute Quasi-Concave Choice Functions," Papers 1805.06632, arXiv.org.
    7. Erick Delage & Jonathan Yu-Meng Li, 2018. "Minimizing Risk Exposure When the Choice of a Risk Measure Is Ambiguous," Management Science, INFORMS, vol. 64(1), pages 327-344, January.
    8. Wei Wang & Huifu Xu, 2023. "Preference robust state-dependent distortion risk measure on act space and its application in optimal decision making," Computational Management Science, Springer, vol. 20(1), pages 1-51, December.
    9. Jonathan Yu-Meng Li, 2021. "Inverse Optimization of Convex Risk Functions," Management Science, INFORMS, vol. 67(11), pages 7113-7141, November.

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