On the global minimization of the value-at-risk

Abstract

In this article, we consider the nonconvex minimization problem of the value-at-risk (VaR) that arise from financial risk analysis. By considering this problem as a special linear program (LP) with linear complementarity constraints (a bilevel LP to be more precise), we develop upper and lower bounds for the minimum VaR and show how the combined bounding procedures can be used to compute the latter value to global optimality. A numerical example is provided to illustrate the methodology.

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