A Class Of Mean-Variance Distributionally Robust Optimization Problems

This thesis considers a class of mean variance distributionally robustoptimization problems in which the set of distributions are defined by the first moments and the bound of second-order moments. With the help of the Lagrange duality theorem, it is demonstrated that the distributionally robust optimization problems are equivalent to linear SDP problems, so that they can be solved by conventional SDP solvers. The reasonability and validity of the proposed model by numericalsimulationsto portfolio applications.The contents of the thesis are summarized as follows:1. Chapter1introduces the research development of portfolio investment, robust optimization and distributionally robust optimization. After that, the mean-variance distributionally robust optimization models are given, which will be mainly studied in this thesis.2. Chapter2presents some preliminaries in matrixanalysis, probability and dual-ity theory.3. In Chapter3, we consider the distributionally robust mean-variance optimiza-tionmodel with uncertainty occurs in the risk constraint only. We prove that the mathematical model is equivalent to a linear SDP problem. We make numerical sim-ulation tests by using the Matlab toolbox YAMLIP, and thenumerical results show good performance of the model.In the application toportfolios, investment weights which calculated by the model are reasonable.4. In Chapter4, we consider the distributionally robust mean-variance optimiza-tionmodel with uncertainty occurs not only in the risk constraint but also in the objective function. The model consists of the constraints on risk-free assets and the fees-taxes, too. Comparing this model with the model in Chapter3, we find that this model has advantages in avoiding risk and it has better robustness.