On the Global Minimization of the Value-at-Risk

Jong-Shi Pang (pangjrpi.edu)
Sven Leyffer (leyffermcs.anl.gov)

Abstract: 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.

Keywords:

Category 1: Complementarity and Variational Inequalities

Category 2: Global Optimization

Category 3: Nonlinear Optimization

Citation: Preprint ANL/MCS-P1112-1203, Argonne National Laboratory, Argonne, IL 60439, December 2003

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Entry Submitted: 12/22/2003
Entry Accepted: 12/23/2003
Entry Last Modified: 12/22/2003

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