Portfolio Selection Based On Possibilistic And Credibilistic Theory

With the constant rapid development of global economy,finance industry has stepped into an era of vigorous development,where various financial derivatives are created.As an indispensable part of quantitative investment field,portfolio selection is drawing the attention of more and more investors,which is significantly promotive to the development of financial investment field.This paper reviews portfolio selection theory in domestic and overseas and has a detailed description over it on the basis of Markowitz's mean-variance model.In addition,single-period and multi-period portfolio selection models are formulated within the framework of possibility and credibility theory.On the basis of this,some effective algorithms are designed to obtain the optimal portfolio.The explicit work is as follows(1)Redefine the concept of mean,variance and skewness of fuzzy numbers within the framework of possibility theory,and formulate a possibilistic single-period mean-variance-skewness portfolio selection model.Within the framework of possibility theory,this work redefines the concepts of mean and variance for fuzzy numbers.Furthermore,this work proposes the concept of skewness and prove some desirable mathematical properties.A fuzzy mean-variance-skewness portfolio selection model is formulated and two variations are given.Some numerical examples are proposed to illustrate the effectiveness of the possibilistic single-period mean-variance-skewness portfolio selection model.(2)Research the product of positive fuzzy numbers within the framework of possibility theory,and formulate a possibilistic multi-period mean-variance-skewness portfolio selection model.To improve the efficiency of algorithm in multi-period portfolio selection,this work studies the product of fuzzy numbers within the framework of possibility theory,proves the related theorems and designs a numerical integral algorithm which can simulate the expected value,variance and skewness of fuzzy numbers.A numerical integral based genetic algorithm is designed to tackle the multi-period portfolio selection problem.The empirical research reveals the algorithm runs faster and can obtain a more efficient investment strategy.(3)Formulate a multi-period mean-variance portfolio selection model within the framework of credibility theory.This work considers a credibilistic multi-period portfolio selection problem with different investment horizons.Compared with the traditional studies assuming that assets have the same investment horizon,this work handles the practical but complicated situation in which assets have different investment horizons.A fuzzy simulation based genetic algorithm is designed to obtain the optimal investment strategy.These three parts are studied within different theories,with innovations of theory in each part.New theorems are proved and innovative algorithms are proposed to obtain the optimal investment strategy.