Werner Römisch, Humboldt-University Berlin
(SPEPS)
Institute for Operations Research and the Management Sciences (Linthicum, Md.)
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| edoc-Server der Humboldt-Universität zu Berlin |
| Author(s): |
Svetlozar T. Rachev, University of California and University of Karlsruhe Werner Römisch, Humboldt-University Berlin | Title: | Quantitative stability in stochastic programming – The method of probability metrics |
| Date of Acceptance: | 20.12.2000 |
| Submission Date: | 04.12.2000 |
| Series Title: |
Stochastic Programming E-Print Series (SPEPS) |
| Editors: | Julie L. Higle; Werner Römisch; Surrajeet Sen |
| Keywords (eng): | quantitative stability, Stochastic programming, probability metrics, Fortet-Mourier metrics, empirical approximations, two-stage models, chance constrained models, stable portfolio models |
| Appeared in: |
Mathematics of operations research 4 (Vol. 27, 2002)
Institute for Operations Research and the Management Sciences (Linthicum, Md.) |
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Endnote Bibtex |
| Abstract (eng): | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Quantitative stability of optimal values and solution sets to stochastic programming problems is studied when the underlying probability distribution varies in some metric space of probability measures. We give conditions that imply that a stochastic program behaves stable with respect to a minimal information (m.i.) probability metric that is naturally associated with the data of the program. Canonical metrics bounding the m.i. metric are derived for specific models, namely, for linear two-stage, mixed-integer two-stage and chance constrained models. The corresponding quantivative stability results as well as some consequences for asymptotic properties of empirical approximations extend earlier results in this direction. In particular, rates of convergence in probability are derived under metric entropy conditions. Finally, we study stability properties of stable investment portfolios having minimal risk with respect to the spectral measure and stability index of the underlying stable probability distribution. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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