Research On Fuzzy Portfolio Model Based On Subjective Factors Of Investors

The securities market is an extremely complicated system.On the one hand,in addition to objective factors,it is inevitable that investors will be influenced by the subjective factors.On the other hand,the uncertainty of the returns and risks in the securities market mainly includes random uncertainty and fuzzy uncertainty.At the same time,we noticed that the research on investment portfolio under the random environment is quite mature.Therefore,We need to study the fuzzy portfolio based on the subjective factors of investors.In an environment of fuzzy uncertainty,this paper studies the portfolio problems based on fuzzy set theory,probability theory,weighting possibility theory,fuzzy decision theory and m_? measurement under the environment of fuzzy uncertainty.The main contents of this paper are as follows:(1)To study the impact of three different risk attitudes on the portfolio of investors.The rate of return is regarded as a trapezoidal fuzzy number,and the risk adaptation value k is introduced into the membership function,that is,the different k values correspond to different risk attitudes.Based on the probability theory,derived the mean,variance and covariance expressions of risk adaptation value.On the basis of this,the mean-variance model of three different risk attitudes is constructed by considering the transaction costs,the investment ratio limitation and the allowable partial investment.Finally,numerical examples are used to compare and analyze change of k value under three different risk attitudes?the influence of different k values under the same risk attitude and the impact of transaction costs on the portfolio.(2)To study the impact of investor preferences on portfolio choices.Different investors have different preferences for returns and risks,whereas different weights correspond to different returns and risks.We discuss three kinds of special weight functions under three different forms and deduce the mean,variance and covariance expressions of weights corresponding to different weight functions.We also construct a bi-objective model of weight mean-variance and numerical examples are used to compare and analyze the Influence of weighting function on portfolio.The results show that three different forms of weight functions correspond to different portfolio selection;despite the same form of portfolio weight function corresponding to the selection are not the same,but the same appetite of investors.Therefore,investors can choose different weight functions to make investment decisions based on their preference for returns and risks.(3)To study the impact of portfolio that investors can not give a precise study of the investment ratio.Considering the proportion of investment as fuzzy number,discussing the case that the rate of return and the investment proportion are triangular fuzzy numbers and trapezoidal fuzzy numbers,the returns and variance expressions of fuzzy investment portfolio are deduced.At the same time,considering the asset liquidity and elastic constraint conditions,constructing multi-objective fuzzy portfolio model,and using fuzzy linear programming to convert the model into parametric linear programming problem.Finally,the feasibility of the model is compared with examples.(4)To study the influence of two subjective factors on the portfolio.Considering that investors are not in completely rational circumstances and introducing optimistic and pessimistic coefficient ? and risk attitude coefficient ?.The larger the value of ?,the more optimistic investors are;the smaller the value of ?,the more pessimistic investors are.The larger the value of ?,the more risky investors are;the smaller the value of ?,the less risky investors are.This paper constructs a fuzzy portfolio model with investors'optimism and pessimism coefficient and risk attitude by using the ?-mean measure to measure the return and the distance measure to measure the degree of dispersion of the fuzzy numbers.Finally,the genetic algorithm is used to solve the model,and the validity of the model is analyzed and compared.In a word,we study the influence of subjective factors on the investment portfolio of investors under fuzzy environment.This study enriches the research of portfolio under fuzzy environment,also has important theoretical and practical significance.