A Class Of Distributionally Robust Quadratic Programming Problems

Distributionally Robust Optimization Problems consider the portfolio’s nondeterminacy in the basic of robust Optimization Problems. As an extention to Markovitz’s expectation-variation model, this paper discuss a class of distributionally robust quadratic programming problems. With the help of duality theory, we show that this class of problems are equivalent to a class of tractable convex quadratic SDP programming problems. Numerical results are reported to show that the solutions obtained by the distributionally robust optimization model are reasonable.The main results of this dissertation are summarized as follows:1. Chapter 1 first gives a background survey about the distributionally robust optimization and the Markowitz portfolio model, including its background and development. Then we propose a class of distributionally robust quadratic programming problems, which will be studied in this thesis.2. In Chapter 2, we introduce some preliminaries about matrices and probability as well as the duality theory, which will be used in this thesis.3. In Chapter 3, we demonstrate that the problems corresponding to those uncertainty structures can be turned to convex quadratic programs, and this result is obtained by using the Lagrange duality method to deal with both the objective function and the constraint function.4. In Chapter 4, we make numerical tests by using the Matlab toolbox YALMIP to verify the performance of the proposed model. After that we analyze numerical example and find that the robust optimization model has advantages over the normal distribution portfolio model in avoiding risk. Then, we compare the model only in the risk constraint with this model,we find this model has better robustness.