Bi-level optimization approach for robust mean-variance problems

Portfolio Optimization is based on the efficient allocation of several assets, which can get heavily affected by the uncertainty in input parameters. So we must look for such solutions which can give us steady results in uncertain conditions too. Recently, the uncertainty based optimization problems are being dealt with robust optimization approach. With this development, the interest of researchers has been shifted toward the robust portfolio optimization. In this paper, we study the robust counterparts of the uncertain mean-variance problems under box and ellipsoidal uncertainties. We convert those uncertain problems into bi-level optimization models and then derive their robust counterparts. We also solve a problem using this methodology and compared the optimal results of box and ellipsoidal uncertainty models with the nominal model.