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Wozabal, David; Hochreiter, Ronald; Pflug, Georg Ch.

A difference of convex formulation of value-at-risk constrained optimization. (English) Zbl 1196.90088

Optimization 59, No. 3-4, 377-400 (2010).
Summary: 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.

Cited in 15 Documents

MSC:

90C15 Stochastic programming
91G10 Portfolio theory
91G80 Financial applications of other theories
90C26 Nonconvex programming, global optimization

Keywords:

stochastic programming; portfolio optimization; D.C. optimization; branch-and-bound
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