Robust order execution under box uncertainty sets

Order execution for algorithmic trading has been studied in the literature as a means of determining the optimal strategy by minimizing a trade-off between expected execution cost and risk. However, the variance has been recognized not to be practical since it is a symmetric measure of risk and, hence, penalizes the low-cost events. In this paper, we propose the use of the conditional value-at-risk (CVaR) of the execution cost as risk measure for the multiple assets case order execution problem. In addition, for the particular box-type parameter estimation errors, we extend both the existing mean-variance approach and our proposed CVaR approach to their robust designs.