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Stochastic Optimization Problems with CVaR Risk Measure and Their Sample Average Approximation

Author

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  • F. W. Meng

    (National University of Singapore)

  • J. Sun

    (National University of Singapore)

  • M. Goh

    (National University of Singapore
    University of South Australia)

Abstract

We provide a refined convergence analysis for the SAA (sample average approximation) method applied to stochastic optimization problems with either single or mixed CVaR (conditional value-at-risk) measures. Under certain regularity conditions, it is shown that any accumulation point of the weak GKKT (generalized Karush-Kuhn-Tucker) points produced by the SAA method is almost surely a weak stationary point of the original CVaR or mixed CVaR optimization problems. In addition, it is shown that, as the sample size increases, the difference of the optimal values between the SAA problems and the original problem tends to zero with probability approaching one exponentially fast.

Suggested Citation

  • F. W. Meng & J. Sun & M. Goh, 2010. "Stochastic Optimization Problems with CVaR Risk Measure and Their Sample Average Approximation," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 399-418, August.
    • Handle: RePEc:spr:joptap:v:146:y:2010:i:2:d:10.1007_s10957-010-9676-3
    DOI: 10.1007/s10957-010-9676-3
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    References listed on IDEAS

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    Cited by:

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    5. Hailin Sun & Huifu Xu & Yong Wang, 2014. "Asymptotic Analysis of Sample Average Approximation for Stochastic Optimization Problems with Joint Chance Constraints via Conditional Value at Risk and Difference of Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 257-284, April.
    6. Sojung Kim & Stefan Weber, 2020. "Simulation Methods for Robust Risk Assessment and the Distorted Mix Approach," Papers 2009.03653, arXiv.org, revised Jan 2022.

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