Practical algorithms for value-at-risk portfolio optimization problems

This article compares algorithms for solving portfolio optimization problems involving value-at-risk (VaR). These problems can be formulated as mixed integer programs (MIPs) or as chance-constrained mathematical programs (CCMPs). We propose improvements to their state-of-the-art MIP formulations. We also specialize an algorithm for solving general CCMPs, featuring practical interpretations. We present numerical experiments on practical-scale VaR problems using various algorithms and provide practical advice for solving these problems.