| Portfolio optimization is to allocate some assets effectively in a complex and uncertain environment,so as to maximize the return and minimize the risk.Distributionally robust optimization has been widely used in the field of portfolio in recent years.The main idea of the distributionally robust optimization method is to construct a set of distribution uncertainties,and assume that the real probability distribution of random variables lies in the set of distributed uncertainties,then calculate the optimal solution of the worst-case objective function.This paper mainly studies a kind of distributionally robust optimization model for solving portfolio problems and some special properties: Based on the constraints such as mean zero-net adjustment,a new distribution uncertainty set is constructed,the corresponding distributionally robust portfolio optimization model is studied,and the influence of parameter value of distribution uncertainty set on decision-making is analyzed.The main contents of this paper are as follows:1.Based on the work of operations research(2010)and the constraint of zero net adjustment of mean value,a new set of distributed uncertainties is constructed.On this basis,the corresponding distributed robust portfolio optimization model is given.Then,the model is further equivalent to a semi-definite programming problem which is easy to be solved by using the relevant optimization theory such as Lagrange duality.2.This paper analyzes the influence of the parameter value of distribution uncertainty set on decision-making,and gives the conclusion and theoretical proof.Furthermore,based on the actual historical data,a numerical experiment is carried out with MATLAB programming.The numerical results confirm the conclusion of theoretical analysis.3.Furthermore,the zero-net adjustment constraint of mean value is relaxed,and the corresponding distributionally robust optimization model is constructed to solve the portfolio problem.When the relaxation parameter is zero,the model is the same as the new model constructed above.The numerical experiment is carried out by using the market historical data,and the comparison is made with the existing model.In Chapter 1,we introduce some existing work related to portfolio and robust optimization;in Chapter 2,we briefly introduce the work and duality theory of Kang et al.and Delage et al;in Chapter 3,we construct a distributionally robust portfolio optimization model with mean zero-net adjustment constraints,and then give the equivalent semi-definite programming form.On this basis,the relationship between the uncertain centralized parameter value and the optimal decision is studied,and then it is verified by numerical experiments.In Chapter 4,the distributionally robust portfolio optimization model based on the relaxation mean zero-net adjustment constraint is studied,and compared with the existing model.Finally,the summary and prospect are given. |
