Stochastic linear programming with a distortion risk constraint - Pavel Bazovkin; Karl Mosler (University of Cologne, Seminar of Economic and Social Statistics, 2011)
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.
Keywords: 330; Robust optimization; data depth; weighted-mean trimmed regions; central regions; coherent risk measure; spectral risk measure; Stochastischer Prozess; Mathematische Optimierung; Risikomaß; Theorie