Fuzzy Random Portfolio Selection Models With Investors' Subjective Attitude

Nowadays,Modern Portfolio Theory has two branches: one is for Markowitz portfolio selection model for cornerstone asset allocation,according to probability theory with pure quantitative approach to measuring the asset return and risk.However,Markowitz's model assumes that in extremely harsh conditions,one of the most central and criticism is the most efficient markets and rational hypothesis.With the development of financial and securities markets,a large number of empirical studies found that human behavior,psychological and subjective factors play an important role in the financial investment,investors are not entirely rational,financial markets are not effective.This led researchers focus on the behavior,behavioral finance,development of portfolio theory accordingly–another important branch of behavioral portfolio theory.Behavioral portfolio primarily through the analysis of the financial markets in the main market of biases and beliefs to seek experience in different markets in different environment theory and decision making behavior,sought to establish a practical decision accurately reflects the market behavior and descriptive models of market health.How using classic investment combination theory of quantitative thought,will behavior investment combination in the market of non-effectiveness and investors of limited rational for quantitative,and will market Shang actual exists of fuzzy uncertainty and random uncertainty,and investors of psychological and behavior deviation reflect to classic of investment combination select model in the,is solution problem of key,is objective,and accurate,and effective to building investment combination select strategy of important based work.This thesis considers investor of rational and non-rational and irrational,market efficiency and non-validation and incomplete validation using fuzzy random theory to construct a series of model for portfolio selection,these models can help investors in fuzzy and stochastic double making portfolio decisions under uncertainty.Taking into account the investors' personal preferences and biases(including investors pessimistic,rational,emotional levels and risk preference)on the basis of subjective factors such as,we further investigated with a variety of constrained portfolio selection model conditions.Taking into account minimum trading number of lots,the minimum investment amount restriction,whether to allow borrowing the risk-free asset,whether to allow the buying,selling and the total investment amount limits and other objective constraints.Finally,the model is applied to the reality of the financial markets,the effectiveness and stability.Major innovation of this paper includes the following aspects:(1)First,we defined a series of new crisp numerical characteristics of fuzzy random variables,including the upper and lower possibilistic expected values,the interval possibilistic expected value and the crisp possibilistic expected value,the upper and lower possibilistic variances and the crisp possibilistic variance,and the possibilistic covariance.Those definitions are consistent with probability theory and fuzzy sets extension principle.They are considered both fuzziness and randomness simultaneously.At the same time we have also discussed their properties,and proved that those properties are as good as in probability theory,such as the linear nature.We have exhibited some typical examples to illustrate the method of how to calculate these numerical characteristics of fuzzy random variables.Then,we studied the risk asset portfolio selection problem under fuzzy random environment.By using fuzzy random variables characterize the rate of return of risk assets,the establishment of a general fuzzy stochastic mean-variance portfolio model with risky assets investment proportion constraints,the model includes the conditions of whether to allow short selling and investment proportion lower bound constraints.On this basis,put forward the concrete portfolio optimization model with trapezoidal fuzzy random rate of return,the model can be transformed into solving a quadratic programming problems.The model makes an empirical analysis of 9 stocks in Shanghai 50 index,the results show that the model can effectively disperse the non-system risk.(2)Second,considering that there are two kinds of uncertainties: fuzziness and randomness.The purpose of our research is to analyze the impact of investors' psychology and behavior to the future return rates.The return rates of securities can be regarded as fuzzy random variables under the condition of non-completed-efficient market and bounded investors.We propose a new definition of weighed expectation,weighed variance and weighed covariance to measure return and risk of portfolio.The new measurements can reflect investors' subjective attitudes to the return and risk by parameter.By solving a parameter quadratic programming,different investors can obtain different efficient frontiers suitable for each of them.Empirical analysis shows that the proposed model is better than Markowitz's M-V model and superior to ?-mean-variance model proposed by Li et.al..(3)Third,we introduced new measurements of return and risk for portfolio selection problem by fuzzy-random theories based on investors' psychology and behaviors.A fuzzy random portfolio selection model with investors' optimistic & pessimistic level ?,rational & emotional degree ?is proposed for different attitude investors based on the assumptions of market inefficiency and investors bounded rationality.The new method provides a efficient way to reflect investors' subjective attitudes and investment actions in the stock market which includes fuzzy and random uncertainties simultaneously.Different investors can obtain different investment strategies by setting different value of parameters ? and ?.A numerical example is presented to illustrate the effectiveness and superiority of the more flexible new method.(4)Finally,in financial markets,investors' psychology and behavior may affect stock price and return directly or indirectly.Different from the assumption of Markowitz's M-V model,this paper deals with portfolio selection problem with investors psychology and behavior under the condition of fuzzy random uncertain environment,in which the assumption is that investors are boundedly rational and stock market is weakly efficient.The future return of assets is not only related to historical return but also connected with investors' judgements to the multiple new information.A new fuzzy random expectation return of portfolio with three parameters is proposed,in which parameters ?,? and s represent investors optimistic-pessimistic level,rational-emotional degree and risk-preference grade,respectively.A new possibilistic standard deviation is introduced to characterize risk of portfolio.Based on the new measurements,a novel(?,?,s)-mean-standard-deviation model is obtained,which is a parametric linear programming model.A numerical example is given to illustrate the application of proposed model and demonstrate the diversity of the strategies.The results show that different investors with different objective attitudes will have different efficient frontiers.