A Class Of Distributionally Robust Portfolio Selection Problems With CVaR Constraints

This thesis studies a class of distributionally robust portfolio selection problems with con-ditional value-at-risk (CVaR) constraints, in which the objective is to maximize worst-case re-turns with controlling CVaR. The distribution set is bounded by the first-order moment and the second-order moment’s upper bound related to the return on investment. With the help of mo-ment theory and duality theory, we prove that the problem can be expressed by a semidefinite programming. We can use the MATLAB to obtain the optimal portfolio and the relevant condi-tional value-at-risk. The numerical results are reported to show that the distributionally robust optimization model is reasonable and effective.The main contents of this thesis are summarized as follows:1. Chapter 1 introduces the research development of the robust portfolio problem and the portfolio theory based on the VaR and CVaR. Finally, the distributionally robust optimization problem with CVaR constraints is given, which will be mainly studied in this thesis.2. Chapter 2 presents some preliminaries about moment theory, duality theory and condi-tional value-at-risk.3. Chapter 3 is the main part of this thesis. We firstly present the distributionally robust optimization model with CVaR constraints, and then we prove that the mathematical model is equivalent to a SDP problem.4. In chapter 4, we make numerical simulation tests by using the MATLAB toolbox YALMIP, the numerical results show the relationship between the confidence level and con-ditional value-at-risk. Finally, we present some other models and illustrate the effectiveness of the distributionally robust optimization model on risk management.