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A difference of convex formulation of value-at-risk constrained optimization

D. Wozabal (david.wozabal***at***univie.ac.at)
R. Hochreiter (ronald.hochreiter***at***univie.ac.at)
G. Ch. Pflug (georg.pflug***at***univie.ac.at)

Abstract: In this article, we present a representation of value-at-risk (VaR) 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 VaR 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: D. Wozabal, R. Hochreiter, and G. Ch. Pflug. A D.C. Formulation of Value-at-Risk constrained optimization. Optimization, Volume 59(3), 377-400, 2010

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Entry Submitted: 01/03/2008
Entry Accepted: 01/03/2008
Entry Last Modified: 01/27/2011

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