Computational aspects of minimizing conditional value-at-risk

We consider optimization problems for minimizing conditional value atrisk (CVaR) from a computational point of view, with an emphasis on financial applications. As a general solution approach, we suggest to reformulate these CVaR optimization problems as twostage recourse problems of stochastic programming. Specializing the L shaped method leads to a new algorithm for minimizing conditional valueatrisk. We implemented the algorithm as the solver CVaRMin. For illustrating the performance of this algorithm, we present some comparative computational results with two kinds of test problems. Firstly, we consider portfolio optimization problems. Such problems, involving conditional value at risk, play an important role in portfolio optimization and financial risk management. Therefore, besides testing the performance of the proposed algorithm, we also present computational results of interest in finance. In our experiments, the instances of the portfolio optimization problem involve 5 random variables representing asset classes. Secondly, with the primary aim of testing algorithm performance, we also present comparative computational results with randomly generated test problems involving 50 random variables. In all of our tests, the experimental solver, based on the new approach, outperformed by at least one order of magnitude all generalpurpose solvers, with an accuracy of solution being in the same range as that with the LP solvers.