Stochastic linear programming with a distortion risk constraint
by Pavel Bazovkin ; Karl Mosler
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
Year of publication: |
2011
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Authors: | Bazovkin, Pavel ; Mosler, Karl C. |
Publisher: |
Köln : Univ., Seminar für Wirtschafts- und Sozialstatistik |
Saved in:
Extent: | 24 S. : graph. Darst, |
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Series: | Discussion papers in statistics and econometrics. - Köln : Seminar f. Wirtschafts- u. Sozialstatistik, Univ. zu Köln. - Vol. 2011,6 |
Type of publication: | Book / Working Paper |
Language: | English |
Source: |
Persistent link: https://www.econbiz.de/10009495859
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