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Erscheinungsjahr: 
2022
Quellenangabe: 
[Journal:] Journal of Global Optimization [ISSN:] 1573-2916 [Volume:] 84 [Issue:] 2 [Publisher:] Springer US [Place:] New York, NY [Year:] 2022 [Pages:] 255-293
Verlag: 
Springer US, New York, NY
Zusammenfassung: 
We discuss stochastic optimization problems under distributional ambiguity. The distributional uncertainty is captured by considering an entire family of distributions. Because we assume the existence of data, we can consider confidence regions for the different estimators of the parameters of the distributions. Based on the definition of an appropriate estimator in the interior of the resulting confidence region, we propose a new data-driven stochastic optimization problem. This new approach applies the idea of a-posteriori Bayesian methods to the confidence region. We are able to prove that the expected value, over all observations and all possible distributions, of the optimal objective function of the proposed stochastic optimization problem is bounded by a constant. This constant is small for a sufficiently large i.i.d. sample size and depends on the chosen confidence level and the size of the confidence region. We demonstrate the utility of the new optimization approach on a Newsvendor and a reliability problem.
Schlagwörter: 
Data-driven stochastic optimization
Bayesian approach
Distributional ambiguity
Distributionally robust stochastic optimization
Newsvendor problem
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