Intuitionistic Fuzzy Portfolio Selection Based On Prospect Theory And Entropy-Weighted Method With Parameter

Most of the existing portfolio studies use the historical return data of securities to predict the expected return and risk,and then construct the portfolio selection model.However,in reality,there are many securities with insufficient historical data.Due to its new listing or data loss,it is difficult for investors to obtain sufficient historical data to accurately predict the expected return and risk,so that the existing model will be ineffective.To solve this problem,this paper proposes the entropy-weighted method with parameter and the weighted closeness coefficient,and then constructs a new kind of securities evaluation system based on the multi-attribute decision-making method.In addition,this paper combines prospect theory with intuitionistic fuzzy theory,defines the prospect value function and the prospect consistency coefficient to deeply study the influence of investors' irrational factors in investment decision-making:(1)This paper improves the classical distance measures of intuitionistic fuzzy set to overcome its shortcoming of deviating from the transitivity rule in the strict axiomatic definition,and then defines the characteristic function of distance measure to analyze the problem and provide the corresponding solution when the function is continuous.Considering that intuitionistic fuzzy set can evaluate securities from both pro and con,it is more suitable to use intuitionistic fuzzy set for the quantitative evaluation of securities in the uncertain market environment.However,in the difference calculation of intuitionistic fuzzy sets,the classical Hamming distance measure and Euclidean distance measure cannot meet the transitivity rule in the strict axiomatic definition.This will lead to the inconsistency between the calculation results and the reality,and then provide the imprecise securities evaluation.Therefore,this paper improves these two distance measures.Besides,the characteristic function is defined to deeply study the possible problem of the distance measure with continuous characteristic function,and then the corresponding solution is put forward.(2)This paper proposes the entropy-weighted method with parameter,and modifies the TOPSIS method to establish a comprehensive securities evaluation system.First of all,to evaluate the securities with insufficient historical data,investors should obtain some related information from other places.In this case,investors may not fully trust the information.In order to combine the investors' cognition of information and then adjust the weights for criteria,this paper improves the traditional entropy-weighted method,puts forward the entropy-weighted method with parameter,and proves the rationality of the method through its mathematical properties;secondly,the positive and negative ideal solutions in TOPSIS method is redefining to make it more similar to return and risk and enhance its applicability in portfolio selection;finally,the risk preference parameter is introduced into the closeness coefficient,so that the securities evaluation system can provide investors with more suitable results according to their risk preference,and the flexibility of TOPSIS method is improved.(3)Based on the intuitionistic fuzzy theory and prospect theory,the intuitionistic fuzzy prospect value function is defined,and the prospect consistency coefficient is proposed.On this basis,this paper constructs the intuitionistic fuzzy mean-variance model.Generally,investors will have an initial impression and cognition of securities while they obtaining securities information.And according to prospect theory,this kind of cognition is irrational,which reflects investors' preference for securities to some extent.If the deviation between an investment strategy and the preference cognition is obvious,investors may think that the model is ineffective,and then reject the optimal strategy provided by the model.Therefore,in this paper,the intuitionistic fuzzy prospect value function is defined to describe investors' preference for securities,and the prospect consistency coefficient is proposed to quantify the difference between investment strategy and investors' preference for securities.Finally,the expression of portfolio return and risk in intuitionistic fuzzy environment is put forward,and the intuitionistic fuzzy mean-variance model with the prospect consistency constraint is constructed.This model can provide investors with optimal portfolio strategy,which is consistent with their risk preference and security preference.In summary,this paper focuses on the problem of insufficient historical data,researches on the construction of securities evaluation system and that of intuitionistic fuzzy portfolio model.In theory,it improves the distance measure of intuitionistic fuzzy sets,optimizes the positive and negative ideal solutions of TOPSIS method,and then provides more reliable theoretical support for their practical application;in application,this paper puts forward the entropy-weighted method with parameter,the weighted closeness coefficient and the prospect consistency coefficient.These new methods and definitions take the investor's trust index,risk preference and security preference into account,and then greatly improve the flexibility and effectiveness of the model.The results can not only enrich the fuzzy portfolio theory,but also further expand the behavioral finance theory,and provide theoretical reference and empirical basis for related research fields.