Stability of multistage stochastic programs

Holger Heitsch; Werner Römisch; Cyrille Strugarek

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SPEPS Preprint

Author(s):	Holger Heitsch, Humboldt-University Berlin Werner Römisch, Humboldt-University Berlin Cyrille Strugarek, EDF R&D OSIRIS
Title:	Stability of multistage stochastic programs
Date of Acceptance:	08.08.2005
Submission Date:	30.05.2005
Series Title:	Stochastic Programming E-Print Series (SPEPS)
Editors:	Julie L. Higle; Werner Römisch; Surrajeet Sen
Complete Preprint:	pdf (urn:nbn:de:kobv:11-10059923)
Keywords (eng):	stability, Stochastic programming, multistage, nonanticipativity, filtration, probability metrics
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Abstract (eng):

Quantitative stability of linear multistage stochastic programs is studied. It is shown that the infima of such programs behave (locally) Lipschitz continuous with respect to the sum of an $L_r$-distance and of a distance measure for the filtrations of the original and approximate stochastic (input) processes. Various issues of the result are discussed and an illustrative example is given. Consequences for the reduction of scenario trees are also discussed.

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