The Study On Distributionally Robust Portfolio Selection Problem Under Uncertainty

The trend of economic globalization and financial integration has promoted the connection between China and the international financial community,and a series of financial products such as stocks and futures has gradually penetrated into people's lives.At the same time,with the development of the market economy,the national economic income has continued to raise,the consciousness of national investment has continued to increase,and the demand of finance and investment has increased dramatically.Investors always want to find the optimal portfolio strategy to ensure maximum investment returns among many choices.However,the complex fi-nancial market is highly unstable under the influence of many factors,such as politics,economy and so on.It further leads to the uncertainty of the securities return information and exposes investors to huge investment risks.Therefore,it is of great practical significance for investors to study the problem of portfolio selection under uncertaintySince optimal portfolio strategy depends extremely on the distribution of uncertain returns in financial optimization problem,it is necessary to find an appropriate optimization method when the distribution information is ambiguous.As a novel modeling paradigm,the distri-butionally robust optimization method can effectively deal with the inaccuracy contained in the distribution,so this thesis uses the distributionally robust optimization method to study the problem of portfolio selection.Specifically,a robust ambiguous chance constrained opti?mization model is first established.When the distribution of uncertain returns has supporting information,two new types of perturbation sets are constructed:one is the intersection of ball and budget,and the other is the intersection of ellipsoid and generalized budget.On the basis of two types of perturbation sets,a robust counterpart approximation with ambiguous chance con-straints is sought,and a computationally tractable cone quadratic portfolio selection model is obtained.In addition,a robust mean-CVaR portfolio selection model is proposed in the context of data-driven.When the distribution information of uncertain returns can only be obtained by observing a limited sample data set,a Wasserstein ambiguous set is constructed.The original model is transformed into a finite-dimensional convex programming model,when the support of Wasserstein ambiguous set is cone.Further,three equivalent forms of the portfolio selection model under three types of support of box,budget,and ellipsoid are discussed.Finally,the numerical experiments and analysis of computational results demonstrate the effectiveness of the proposed method in this thesisThe main contributions of this thesis are summarized as follows:(1)A robust ambiguous chance-constrained optimization model and a data-driven robust mean-CVaR portfolio selec-tion model are established;(2)When the distribution information of uncertain returns cannot be accurately known,two new types of perturbation sets and Wasserstein ambiguous sets are constructed;(3)The safe approximation of the robust ambiguous chance-constrained portfolio selection model is derived based on two new types of perturbation sets.Moreover,an equiva?lent form of the robust mean-CVaR portfolio selection model is presented under the Wasserstein metric;(4)A case study of actual data on the Chinese stock market illustrates the practicality of the method presented in this thesis.