A new method for Value-at-Risk constrained optimization using the Difference of Convex Algorithm (DCA)

David Wozabal(david.wozabalunivie.ac.at)

Abstract: This paper treats a Value-at-Risk constrained Markowitz style portfolio selection problem. The described problem is non-convex stochastic problem and in the case of a discrete probability measure can be reformulated to a difference of convex (D.C.) program. We apply the difference of convex algorithm (DCA) to obtain solutions to the problem. Numerical results comparing the solutions found by the DCA to the respective global optima for relatively small problems as well as numerical studies for real life problems are given.

Keywords: Value-at-Risk, Portfolio Optimization, Global Optimization

Category 1: Global Optimization (Applications )

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

Category 3: Stochastic Programming

Citation: Technical Report TR2008-03, Department of Statistics and Decision Support Systems, University of Vienna. January 2008.

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Entry Submitted: 04/23/2008
Entry Accepted: 04/28/2008
Entry Last Modified: 04/23/2008

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