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Asymptotics of minimax stochastic programs

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  • Shapiro, Alexander

Abstract

We discuss in this paper asymptotics of the sample average approximation (SAA) of the optimal value of a minimax stochastic programming problem. The main tool of our analysis is a specific version of the infinite dimensional delta method. As an example, we discuss asymptotics of SAA of risk averse stochastic programs involving the absolute semideviation risk measure. Finally, we briefly discuss exponential rates of convergence of the optimal value of SAA problems.

Suggested Citation

  • Shapiro, Alexander, 2008. "Asymptotics of minimax stochastic programs," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 150-157, February.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:2:p:150-157
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    References listed on IDEAS

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    1. Alan J. King, 1989. "Generalized Delta Theorems for Multivalued Mappings and Measurable Selections," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 720-736, November.
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    Cited by:

    1. Timothy Christensen & Benjamin Connault, 2019. "Counterfactual Sensitivity and Robustness," Papers 1904.00989, arXiv.org, revised May 2022.
    2. Sungyong Choi & Andrzej Ruszczyński & Yao Zhao, 2011. "A Multiproduct Risk-Averse Newsvendor with Law-Invariant Coherent Measures of Risk," Operations Research, INFORMS, vol. 59(2), pages 346-364, April.
    3. Timothy Christensen & Hyungsik Roger Moon & Frank Schorfheide, 2020. "Robust Forecasting," Papers 2011.03153, arXiv.org, revised Dec 2020.
    4. Dentcheva Darinka & Stock Gregory J. & Rekeda Ludmyla, 2011. "Mean-risk tests of stochastic dominance," Statistics & Risk Modeling, De Gruyter, vol. 28(2), pages 97-118, May.
    5. Choi, Sungyong & Jeon, Sumin & Kim, Jinmin & Park, Kwangtae, 2019. "A newsvendor analysis of a binomial yield production process," European Journal of Operational Research, Elsevier, vol. 273(3), pages 983-991.
    6. Darinka Dentcheva & Spiridon Penev & Andrzej Ruszczyński, 2017. "Statistical estimation of composite risk functionals and risk optimization problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 737-760, August.
    7. Chaolin Yang & Zhenyu Hu & Sean X. Zhou, 2021. "Multilocation Newsvendor Problem: Centralization and Inventory Pooling," Management Science, INFORMS, vol. 67(1), pages 185-200, January.

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