Research On The Robust Portfolio Selection Model And Solution Algorithm

The mean-variance model proposed by Markowitz has played a very important role in promoting the portfolio theory.Although much progress has been made in theory,there is a problem in the portfolio optimization model represented by the mean-variance model.That is,slight fluctuations in input parameters will greatly influence the portfolio decision or lead to infeasible investment strategies in practice.In order to reduce the negative impact of the input parameter uncertainty,the robust portfolio theory has gradually attracted the attention of researchers.Combining with the research status and development trend at home and abroad,the main research contents of this paper include the following three parts:(1)Research on robust minimax regret portfolio selection problem and solution algorithmThis paper uses the minimax regret approach to study the uncertain multi-objective portfolio selection problem and gives its corresponding robust counterpart.The robust minimax regret portfolio selection model with ellipsoidal uncertainty set and the robust minimax regret portfolio selection model with the box uncertainty set are proposed.To obtain the robust minimax regret solution,this study simplifies the model and further discusses the solution algorithm and solving steps based on the relaxation procedure.This study collects the monthly return data of the SSE 50 Index from January 2012 to December 2017,and uses the robust minimax regret portfolio selection model to test the performance and give the investment decision.(2)Robust multi-objective optimization problem based on minimax regret approach and its application in multi-objective portfolio selection problemThis paper studies the uncertain multi-objective programming problem,and a robust optimization model based on minimax regret approach is established under the finite-scenario uncertainty set,box uncertainty set and ellipsoidal uncertainty set is developed.In order to study the uncertain multi-objective programming problem,this paper defines a robust minimax regret(weakly)efficient solution,and gives a solution algorithm based on the relaxation procedure.The issue of portfolio selection has always been a hot topic of research,but it is affected by the uncertainty parameter problem.In order to obtain a robust but not too conservative portfolio decision,with the expected rate of return and the turnover rate are respectively taking values in the finite scenarios uncertainty set,box uncertainty set and ellipsoidal uncertainty set,this paper establishes a robust multi-objective portfolio optimization model based on minimax regret approach.In order to confirm the feasibility of the model,this paper collects the monthly return data in the SSE 50 index from January 2012 to December 2017 in the empirical analysis.(3)Research on robust multi-objective portfolio selection problem considering Yager's entropyBased on the mean-variance model,this paper uses Yager's entropy to describe the dispersion degree of portfolio and establishes a robust multi-objective portfolio selection model.Under the condition that the expected return belongs to the box uncertainty set and the ellipsoidal uncertainty set,this paper studies the uncertain multi-objective portfolio selection problem and discusses its corresponding robust equivalent form.Through the linear weighted method,the robust(weakly)efficient solution for the uncertain multi-objective portfolio selection problem is obtained and the detailed proof process is given.In the empirical analysis,this paper collects the monthly return data of the SSE 50 Index from January 2015 to December 2017,and applies the robust multi-objective portfolio selection model.This paper hopes that the above research can make up for the shortcomings in the existing research,eliminate the gap between the theory and practice of portfolio selection,and provide investors with more attractive and valuable portfolio decision.