Robust Portfolio Selection Based on Optimization Methods

Linear matrix inequalities (LMI) are used to solve robust portfolio problems and many other control problems. Ellipsoid algorithm and interior-point method are used to solve LMI. In this paper, we consider a robust portfolio model based on Markowitz theory that minimizes the risk at a certain level of return. We turn the model into the LMI with constraints and use ellipsoid algorithm and interior-point method to solve it. A numerical simulation in stock portfolio is given to prove the validity of the method. Because the rate of return is change over time, in order to make the result robust, we use exponentially weighted moving-average (EWMA) method to compute the covariance matrices. Due to the highly reliable result, the model can provide a reference for investors to make decision on portfolio.