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Ambiguity in risk preferences in robust stochastic optimization

Author

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  • Haskell, William B.
  • Fu, Lunce
  • Dessouky, Maged

Abstract

We consider robust stochastic optimization problems for risk-averse decision makers, where there is ambiguity about both the decision maker’s risk preferences and the underlying probability distribution. We propose and analyze a robust optimization problem that accounts for both types of ambiguity. First, we derive a duality theory for this problem class and identify random utility functions as the Lagrange multipliers. Second, we turn to the computational aspects of this problem. We show how to evaluate our robust optimization problem exactly in some special cases, and then we consider some tractable relaxations for the general case. Finally, we apply our model to both the newsvendor and portfolio optimization problems and discuss its implications.

Suggested Citation

  • Haskell, William B. & Fu, Lunce & Dessouky, Maged, 2016. "Ambiguity in risk preferences in robust stochastic optimization," European Journal of Operational Research, Elsevier, vol. 254(1), pages 214-225.
    • Handle: RePEc:eee:ejores:v:254:y:2016:i:1:p:214-225
    DOI: 10.1016/j.ejor.2016.03.016
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    Cited by:

    1. Chan, Chi Kin & Zhou, Yan & Wong, Kar Hung, 2019. "An equilibrium model of the supply chain network under multi-attribute behaviors analysis," European Journal of Operational Research, Elsevier, vol. 275(2), pages 514-535.
    2. Wei Wang & Huifu Xu, 2023. "Preference robust distortion risk measure and its application," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 389-434, April.
    3. Yu, Guodong & Haskell, William B. & Liu, Yang, 2017. "Resilient facility location against the risk of disruptions," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 82-105.
    4. Yu, Guodong & Zhang, Jie, 2018. "Multi-dual decomposition solution for risk-averse facility location problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 116(C), pages 70-89.
    5. Mengshi Lu & Zuo‐Jun Max Shen, 2021. "A Review of Robust Operations Management under Model Uncertainty," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1927-1943, June.
    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. Liu, Jia & Chen, Zhiping, 2018. "Time consistent multi-period robust risk measures and portfolio selection models with regime-switching," European Journal of Operational Research, Elsevier, vol. 268(1), pages 373-385.
    8. Zhao, Kena & Ng, Tsan Sheng & Tan, Chin Hon & Pang, Chee Khiang, 2021. "An almost robust model for minimizing disruption exposures in supply systems," European Journal of Operational Research, Elsevier, vol. 295(2), pages 547-559.

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