Argonne National Laboratory

On the Global Minimization of the Value-at-Risk

TitleOn the Global Minimization of the Value-at-Risk
Publication TypeReport
Year of Publication2003
AuthorsPang, J-S, Leyffer, S
Series TitleOptimization Methods and Software
Date Published12/2003
Other NumbersANL/MCS-P1112-1203

In this paper, we consider the nonconvex minimization problem of the value-at-risk (VaR) that arises from financial risk analysis. By considering this problem as a special linear program with linear complementarity constraints (a bilevel linear program 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.