On the Global Minimization of the Value-at-Risk
Optimization and Control
2025-10-20 v1 Numerical Analysis
Numerical Analysis
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
Cite
@article{arxiv.math/0401063,
title = {On the Global Minimization of the Value-at-Risk},
author = {Jong-Shi Pang and Sven Leyffer},
journal= {arXiv preprint arXiv:math/0401063},
year = {2025}
}
Comments
21 pages, 1 figure