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Research On Portfolio Selection Model And Its Application Based On Fuzzy Theory

Posted on:2012-09-26Degree:DoctorType:Dissertation
Country:ChinaCandidate:Y P FuFull Text:PDF
GTID:1119330338954470Subject:Statistics
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In recent years, Introduce the method of fuzzy theory and fuzzy decision to the construction of the portfolio selection model has been one of the issues in the field of portfolio selection. Stock market is a very complicated system, the return and risk of security affected by many factors, such as international and domestic situation, political and economic policies, operating performance of the listed company and natural disaster, etc. These cause the uncertain description of the return and risk of investment. Moreover, the subjectivity of investors is inevitable in decision-making process. In such a complex economy system to make a scientific judgment and rational thinking, the first problem to be solved is how to deal with the uncertain information. And the uncertainty of such information includes two factors:one is the randomness, that is, if the event happens and the probability of occurrence; the other is fuzziness, namely, the complexity of the problems themselves and the vagueness of decision maker's thinking and judgment. So purely from the angle of randomness study on portfolio selection is obviously not comprehensive enough, fuzziness must be taken into account. This paper starting from the point of fuzziness, discusses the acquirement of fuzzy anticipation rate of return, establishes portfolio selection model based on fuzzy theory, study its solution and application. This paper concludes major achievements as follows:(1)To study the portfolio selection based on fuzzy theory, the first thing tobe concerned is how to describe the anticipation return and risk of investment by the use of fuzzy set. This paper proposes one method for acquiring anticipation fuzzy profit rate based on Markov chain. Take the return of investment as a stochastic process meet the conditions for Markov. The range of securities return rate is divided into several state spaces, comprehensive consideration to the fluctuations of stock rate of return in each period, with the help of Markov chain the rate of securities return be represented by fuzzy set. This method of proceeding from historical data, taking into account the fluctuations of each period, the model structuring process does not contain the subjective wishes of investors and any expert experience, the description of the fuzzy rate of return is more objective and reasonable. The rate of return by this method is fuzzy number, and the fuzzy number reflects the fluctuations of stock return every day.(2)This paper takes a new kind of possibilistic variance as the measure of the risk of portfolio selection, establishes possibilistic mean-variance portfolio selection model, studies several kinds of special possibilistic distribution, proposes the specific forms of model and their solutions. After that, the application of this model is given. On the basis of research above, takes risk-free asset, the investment ratio restriction and borrowing constraint into account in the construction of the model. That makes the model structure more complete and closer to the actual application process.(3) Fuzzy Linear Program is introduced to solve the problem of portfolio selection, elastic constraint is introduced to structure model on the basis of Carlsson's possibilistic mean-variance model, fuzzy method is used to solve the possibilistic portfolio selection model with elastic constraint. In this process, elastic constraint is represented by the membership function of fuzzy set, so the elastic constraint can be transformed. The solution of possibilistic portfolio selection model with elastic constraint is transformed into parametric programming problem at last. Then the comparative analysis of possibilistic portfolio selection model and possibilistic portfolio selection model with elastic constraint is given.(4) In the process of defining mean value, variance and covariance of fuzzy number, the investor's different attitudes to different securities are described by the parametric X. The value of the parametricλis greater, the decision maker's attitude is more optimistic, vice versa. When he parametricλis equals 0.5, the possibilistic mean value of fuzzy number is the integrals of the fuzzy number's middle point of left and right endpoint of each cut set. That means the investor's attitude is neutral. Takes this kind of mean value and variance of fuzzy number as the measure of the return and risk of risk assets, establishes possibilistic mean-variance model based onλcut set, studies its solution and its application.(5) Based on the theory of distance in fuzzy space, a new kind of definition of expectation, variance and covariance is introduced when stochastic variables are fuzzy variables. And this paper studies the properties of expectation and variance, explores the specific forms of several kinds of special fuzzy number. Then takes this kind of mean value and variance of fuzzy number as the measure of the return and risk of risk assets, establishes possibilistic mean-variance model based on the theory of distance in fuzzy space, studies its solution and its application.(6) In the end, this paper conducts a comprehensive and in-depth contrast analysis of these four models has proposed, discusses each model's application spectrum and their limitation, analyses the similarities and differences between these four models and the other existing models.
Keywords/Search Tags:Portfolio selection, Markov chain, Fuzzy number, Possibilistic distribution, Possibilistic mean value, Possibilistic variance, Weighted possibilistic mean value, Weighted possibilistic variance, Portfolio selection model
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