A D.C. Formulation of Value-at-Risk constrained Optimization

D. Wozabal (david.wozabalunivie.ac.at)
R. Hochreiter (ronald.hochreiterunivie.ac.at)
G. Ch. Pflug (georg.pflugunivie.ac.at)

Abstract: In this paper we present a representation of Value-at-Risk (V@R) as a difference of convex (D.C.) functions in the case where the distribution of the underlying random variable is discrete and has finitely many atoms. The D.C. representation is used to study a financial risk-return portfolio selection problem with a V@R constraint. A Branch-and-Bound algorithm that numerically solves the problem exactly is given. Numerical experiments with historical asset returns from representative market indices are performed to apply the algorithm to real-world financial market data.

Keywords: Stochastic Programming, D.C. Optimization, Portfolio Optimization, Branch-and-Bound

Category 1: Stochastic Programming

Category 2: Applications -- OR and Management Sciences (Finance and Economics )

Category 3: Global Optimization (Other )

Citation: Technical Report TR2008-01. Department of Statistics and Decision Support Systems, University of Vienna. January 2008.

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Entry Submitted: 01/03/2008
Entry Accepted: 01/03/2008
Entry Last Modified: 01/07/2008

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