A data-driven robust EVaR-PC with application to portfolio management.

Abstract

We investigate the robust chance constrained optimization problem (RCCOP), which is a combination of the distributionally robust optimization (DRO) and the chance constraint (CC). The RCCOP plays an important role in modeling uncertain parameters within a decision-making framework. The chance constraint, which is equivalent to a constraint of Value-at-risk (VaR), is approximated by risk measures such as Entropic Value-at-risk (EVaR) or Conditional Value-at-risk (CVaR) due to its difficulty to be evaluated. An excellent approximation requires both tractability and non-conservativeness. In addition, the DRO assumes that we know partial information about the distribution of uncertain parameters instead of their known true underlying probability distribution. In this article, we develop a novel approximation EVaR- PC based on EVaR for CC. Then, we evaluate the proposed approximation EVaR- PC using a discrepancy-based ambiguity set with the wasserstein distance. From a theoretical perspective, the EVaR- PC is less conservative than EVaR and the wasserstein distance possesses many good theoretical properties; from a practical perspective, the discrepancy-based ambiguity set can make full use of the data to estimate the nominal distribution and reduce the sensitivity of decisions to priori knowledges. To show the advantages of our method, we show its application in portfolio management in detail and give the relevant experimental results.