On The Distribution Robust Optimization Model With CVaR Constraints

In this paper, we are concerned with a distributionally robust optimization model with CVaR constraints whose uncertainty set of distributions is defined by the first-order moment and the upper bound for the second-order moment. With the help of the Lagrange duality theory, the problem is demonstrated to be equivalent to a linear semidefinite programming problem and the conventional Matlab solvers can be used to solve it. 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. Chapter1first gives a brief survey about the distributionally robust optimization and the CVaR constraints, including its background and development. After that we describe the model of distributionally robust optimization model with CVaR constraints, which will be studied in this thesis.2. In Chapter2, we introduce some preliminaries about matrices and probability as well as the duality theory, which will be use in the thesis.3. In Chapter3, we demonstrate that the distributionally robust optimization model with CVaR constraints is equivalent to a linear SDP problem, and this result is obtained by using the Lagrange duality method to deal with both the objective function and the constraint function.4. In Chapter4, we make numerical tests by using the Matlab toolbox YAMLIP to verify the performance of the proposed model. After that we analyze a specific numerical example and find the linear dependence of portfolio profits on both confidence factor and disturbance factor. Finally, we compare the risk values by the distributionally robust optimization model with those by the portfolio model under the normal distribution, and find that the robust optimization model has a big advantage over the normal distribution portfolio model for avoiding the risk.