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Hoelder and Lipschitz stability of solution sets in programs with probabilistic constraints

Please always quote using this URN:urn:nbn:de:0296-matheon-1087
  • We study perturbations of a stochastic program with a probabilistic constraint and r-concave original probability distribution. First we improve our earlier results substantially and provide conditions implying Hölder continuity properties of the solution sets w.r.t. the Kolmogorov distance of probability distributions. Secondly, we derive an upper Lipschitz continuity property for solution sets under more restrictive conditions on the original program and on the perturbed probability measures. The latter analysis applies to linear-quadratic models and is based on work by Bonnans and Shapiro. The stability results are illustrated by numerical tests showing the different asymptotic behaviour of parametric and nonparametric estimates in a program with a normal probabilistic constraint.

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Metadaten
Author:Rene Henrion, Werner Römisch
URN:urn:nbn:de:0296-matheon-1087
Referee:Anton Bovier
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2004/03/29
Release Date:2004/03/29
Institute:Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
Preprint Number:103
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