A Framework for Optimization under Ambiguity

David Wozabal (david.wozabalunivie.ac.at)

Abstract: In this paper, single stage stochastic programs with ambiguous distributions for the involved random variables are considered. Though the true distribution is unknown, existence of a reference measure P enables the construction of non-parametric ambiguity sets as Kantorovich balls around P. The resulting robustified problems are infinite optimization problems and can therefore not be solved computationally. To solve these problems numerically, equivalent formulations as finite dimensional non-convex, semi definite saddle point problems are proposed. Finally an application from portfolio selection is studied for which methods to solve the robust counterpart problems explicitly are proposed and numerical results for sample problems are computed.

Keywords: robust optimization; portfolio management; difference of convex algorithm; semi definite programming; expected shortfall; non-convex optimization; extreme points

Category 1: Global Optimization (Applications )

Category 2: Robust Optimization

Category 3: Stochastic Programming

Citation: David Wozabal. A Framework for Optimization under Ambiguity, Annals of Operations Research 2010, Online First Stable Link: http://dx.doi.org/10.1007/s10479-010-0812-0

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Entry Submitted: 10/17/2008
Entry Accepted: 11/01/2008
Entry Last Modified: 01/27/2011

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