Stochastic linear programming with a distortion risk constraint
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the violation of restrictions. Such a model turns out to be appropriate for many applications and, principally, for the mean-risk portfolio selection problem. Each risk...
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| Sprache: | eng |
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Köln
Univ., Seminar für Wirtschafts- und Sozialstatistik
2011
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| Schriftenreihe: | Discussion papers in statistics and econometrics
2011,6 |
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| Online Zugang: | http://www.wisostat.uni-koeln.de/Forschung/Papers/ORaTR-DiscPaper.pdf |
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Tag hinzufügen | Zusammenfassung: | Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the violation of restrictions. Such a model turns out to be appropriate for many applications and, principally, for the mean-risk portfolio selection problem. Each risk constraint induces an uncertainty set of coefficients, which comes out to be a weighted-mean trimmed region. We consider a problem with a single constraint. Given an external sample of the coefficients, the uncertainty set is a convex polytope that can be exactly calculated. If the sample is i.i.d. from a general probability distribution, the solution of the stochastic linear program (SLP) is a consistent estimator of the SLP solution with respect to the underlying probability. An efficient geometrical algorithm is proposed to solve the SLP. -- Robust optimization ; data depth ; weighted-mean trimmed regions ; central regions ; coherent risk measure ; spectral risk measure |
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| Beschreibung: | 24 S. : graph. Darst, |
| Format: | Acrobat Reader |