| edoc-Server der Humboldt-Universität zu Berlin |
| Author(s): | Christian Küchler, Mathematik | Title: | On Stability of Multistage Stochastic Programs |
| Date of Acceptance: | 02.07.2008 |
| Series Title: |
Stochastic Programming E-Print Series (SPEPS) |
| Editors: | Julie L. Higle; Werner Römisch; Surrajeet Sen |
| Complete Preprint: | pdf (urn:nbn:de:kobv:11-10090074) |
| Keywords (eng): | stability, stochastic programming, multistage, probability metrics |
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| Abstract (eng): | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| We study quantitative stability of linear multistage stochastic programs under perturbations of the underlying stochastic processes. It is shown that the optimal values behave Lipschitz continuous with respect to an $L_p$-distance. Therefore, we have to make a crucial regularity assumption on the conditional distributions, that allows to establish continuity of the recourse function with respect to the current state of the stochastic process. The main stability result holds for nonanticipative discretizations of the underlying process and thus represents a rigorous justification of established discretization techniques. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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