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Quantitative Stability and Empirical Approximation of Risk-Averse Models Induced by Two-Stage Stochastic Programs with Full Random Recourse

Author

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  • Zhiping Chen

    (School of Mathematics and Statistics, Xi’an Jiaotong University & Center for Optimization, Technique and Quantitative Finance, Xi’an International Academy for Mathematics and Mathematical Technology, Xi’an, Shaanxi 710049, P. R. China)

  • He Hu

    (School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, P. R. China)

  • Jie Jiang

    (School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, P. R. China)

Abstract

In this paper, we consider the quantitative stability analysis and empirical approximation of risk-averse models induced by two-stage stochastic programs with full random recourse. We first establish the quantitative stability under the mean-coherent risk measure framework and the expected utility framework, respectively, under suitable probability metrics. Based on the obtained quantitative stability results, we then investigate the empirical approximation to these models, and estimate the rates of convergence for the optimal value and optimal solution set with the aid of Ky Fan distance.

Suggested Citation

  • Zhiping Chen & He Hu & Jie Jiang, 2021. "Quantitative Stability and Empirical Approximation of Risk-Averse Models Induced by Two-Stage Stochastic Programs with Full Random Recourse," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 38(04), pages 1-25, August.
    • Handle: RePEc:wsi:apjorx:v:38:y:2021:i:04:n:s0217595920500566
    DOI: 10.1142/S0217595920500566
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