Fuzzy Portfolio Efficiency Evaluation And Decision Analysis Considering Investor Psychology Based On DEA Method

Before making a scientific and reasonable decision,investors must be accurately aware of the uncertainty in the real investment environment.There is no doubt that the psychological factors of investors play a critical role in the actual investment decision-making process.In the meanwhile,more and more attention has been paid to evaluating the performance of portfolios.As an effective evaluation method,Data Envelopment Analysis(DEA)has gradually attracted the attention of scholars in the portfolio management.However,the existing portfolio performance evaluation methods mostly appear in random environment,and ignore the influence of investor psychological factors.Therefore,based on fuzzy theory,DEA theory and prospect theory,this paper conducts theoretical exploration and applied research on portfolio selection and efficiency analysis.The main contents are as follows:(1)Comprehensively considering the fuzzy uncertainty of stock market and psychological factors of investors,we discuss the portfolio efficiency evaluation problems with risk attitudes in the possibilistic and credibilistic environment based on DEA method.Firstly,the risk attitude parameter k is introduced into the membership function of trapezoidal fuzzy number,and some possibilistic and credibilistic measures with risk attitude are deduced through rigorous mathematical proof.Furthermore,the corresponding return and risk measures are used as the output and input factors of DEA models,and the real constraints such as transaction costs and transaction volume are considered to construct portfolio efficiency evaluation models.Finally,through numerous simulation experiments and correlation analysis,the feasibility and effectiveness of constructed portfolio efficiency evaluation models with investor psychological factors is verified.(2)Combined with DEA game cross-efficiency evaluation method,a multi-objective fuzzy portfolio model with investor psychological factors is designed.Firstly,to fully describer the psychology and risk perception of investors,the possibilistic mean and semi-absolute deviation with risk attitude are used as the return and risk measure respectively.Secondly,the candidate assets are regarded as competing players,and their comprehensive performance is measured by DEA game cross-efficiency model based on entropy weight method.In this way,the DEA game cross efficiency score and maverick index of each asset are obtained.Based on this,by considering the four objectives of possibilistic mean,semi-absolute deviation,cross-efficiency score and the maverick index,a fuzzy portfolio optimization model is established.Finally,the rationality and effectiveness of the proposed model is illustrated by an application example.(3)A new fuzzy portfolio optimization model based on DEA prospect cross-efficiency method is studied.Firstly,in order to incorporate psychological factors into the DEA crossefficiency evaluation,two novel DEA prospect cross-efficiency models-PCE(I)and PCE(II)are designed,which can be seen as improvements and extensions to DEA cross-efficiency evaluation.Furthermore,a novel mean-variance-maverick fuzzy portfolio framework based on the PCE evaluation is proposed.Finally,the empirical analysis shows the practicability and effectiveness of PCE evaluation and MVM model.In a word,based on the DEA method,the fuzzy portfolio efficiency evaluation and optimization models with investor psychology are mainly discussed in this paper.The research results not only enrich the investment portfolio theory,but also have certain practical significance.