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Stability of a class of risk-averse multistage stochastic programs and their distributionally robust counterparts

  • * Corresponding author: Zhiping Chen

    * Corresponding author: Zhiping Chen 

This work is supported by the National Natural Science Foundation of China Grant Numbers 11735011 and 11571270, and the World-Class Universities (Disciplines) and the Characteristic Development Guidance Funds for the Central Universities under Grant Number PY3A058

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  • In this paper, we consider the quantitative stability of a class of risk-averse multistage stochastic programs, whose objective functions are defined by multi-period $ p $th order lower partial moments (LPM) with given targets, and their distributionally robust counterparts. We first derive the upper bounds of feasible solutions as preliminaries. Then, by employing calm modifications, the quantitative stability results are obtained under a special measurable perturbation of stochastic process, which extend the present results under risk-neutral cases to risk-averse ones. Moreover, we recast the risk-averse model by probability measures of stochastic process, and obtain new quantitative stability estimations on the basis of proper probability metrics under the general perturbation of stochastic process. Finally, motivated by the availability of only partial information about probability measures, we further consider the distributionally robust counterpart of our recasting model, and establish the discrepancy of optimal values with respect to the perturbation of ambiguity sets.

    Mathematics Subject Classification: Primary: 90C15, 91B70; Secondary: 93E15.


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  • Figure 1.  Scenario tree for Example 1

    Figure 2.  Scenario trees of $ \mathit{\boldsymbol{\xi}} $ (left), $ f(\mathit{\boldsymbol{\xi}}) $ (central), $ \hat{\mathit{\boldsymbol{\xi}}} $ (right) for Example 2

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