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Robust two-stage stochastic linear optimization with risk aversion

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  • Ling, Aifan
  • Sun, Jie
  • Xiu, Naihua
  • Yang, Xiaoguang

Abstract

We study a two-stage stochastic linear optimization problem where the recourse function is risk-averse rather than risk neutral. In particular, we consider the mean-conditional value-at-risk objective function in the second stage. The model is robust in the sense that the distribution of the underlying random variable is assumed to belong to a certain family of distributions rather than to be exactly known. We start from analyzing a simple case where uncertainty arises only in the objective function, and then explore the general case where uncertainty also arises in the constraints. We show that the former problem is equivalent to a semidefinite program and the latter problem is generally NP-hard. Applications to two-stage portfolio optimization, material order problems, stochastic production-transportation problem and single facility minimax distance problem are considered. Numerical results show that the proposed robust risk-averse two-stage stochastic programming model can effectively control the risk with solutions of acceptable good quality.

Suggested Citation

  • Ling, Aifan & Sun, Jie & Xiu, Naihua & Yang, Xiaoguang, 2017. "Robust two-stage stochastic linear optimization with risk aversion," European Journal of Operational Research, Elsevier, vol. 256(1), pages 215-229.
    • Handle: RePEc:eee:ejores:v:256:y:2017:i:1:p:215-229
    DOI: 10.1016/j.ejor.2016.06.017
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    References listed on IDEAS

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    1. Ang, James & Meng, Fanwen & Sun, Jie, 2014. "Two-stage stochastic linear programs with incomplete information on uncertainty," European Journal of Operational Research, Elsevier, vol. 233(1), pages 16-22.
    2. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    3. Alexandra Künzi-Bay & János Mayer, 2006. "Computational aspects of minimizing conditional value-at-risk," Computational Management Science, Springer, vol. 3(1), pages 3-27, January.
    4. Riis, Morten & Andersen, Kim Allan, 2005. "Applying the minimax criterion in stochastic recourse programs," European Journal of Operational Research, Elsevier, vol. 165(3), pages 569-584, September.
    5. Keiiti Isii, 1960. "The extrema of probability determined by generalized moments (I) bounded random variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 12(2), pages 119-134, June.
    6. Robert Carbone & Abraham Mehrez, 1980. "Note---The Single Facility Minimax Distance Problem Under Stochastic Location of Demand," Management Science, INFORMS, vol. 26(1), pages 113-115, January.
    7. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    8. Steftcho P. Dokov & David P. Morton, 2005. "Second-Order Lower Bounds on the Expectation of a Convex Function," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 662-677, August.
    9. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    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. Dimitris Bertsimas & Xuan Vinh Doan & Karthik Natarajan & Chung-Piaw Teo, 2010. "Models for Minimax Stochastic Linear Optimization Problems with Risk Aversion," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 580-602, August.
    12. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    13. Philpott, A.B. & de Matos, V.L., 2012. "Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion," European Journal of Operational Research, Elsevier, vol. 218(2), pages 470-483.
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    Cited by:

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    2. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2022. "Robust portfolio selection problems: a comprehensive review," Operational Research, Springer, vol. 22(4), pages 3203-3264, September.
    3. Ling, Aifan & Sun, Jie & Wang, Meihua, 2020. "Robust multi-period portfolio selection based on downside risk with asymmetrically distributed uncertainty set," European Journal of Operational Research, Elsevier, vol. 285(1), pages 81-95.
    4. Bei, Xiaoqiang & Zhu, Xiaoyan & Coit, David W., 2019. "A risk-averse stochastic program for integrated system design and preventive maintenance planning," European Journal of Operational Research, Elsevier, vol. 276(2), pages 536-548.
    5. Wang, Weiqiao & Yang, Kai & Yang, Lixing & Gao, Ziyou, 2021. "Two-stage distributionally robust programming based on worst-case mean-CVaR criterion and application to disaster relief management," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 149(C).
    6. Yining Gu & Yicheng Huang & Yanjun Wang, 2024. "Data-Driven Distributionally Robust Risk-Averse Two-Stage Stochastic Linear Programming over Wasserstein Ball," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 242-279, January.
    7. Adrian Gepp & Geoff Harris & Bruce Vanstone, 2020. "Financial applications of semidefinite programming: a review and call for interdisciplinary research," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 60(4), pages 3527-3555, December.
    8. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2021. "Robust Portfolio Selection Problems: A Comprehensive Review," Papers 2103.13806, arXiv.org, revised Jan 2022.

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