| Modern portfolio selection theory originated from the Markowitz's mean-variance model,which considered the trade-off between return and risk by combining probability theory with optimization methods.This method laid the foundation of modern finance.Following Markowitz's standard mean-variance model,many scholars have studied the portfolio selection problem under the framework of probability theory and have achieved fruitful research results.However,in the real financial market,there are a lot of undeterministic factors.In recent years,with the development and perfection of fuzzy set theory,some researchers have begun to use fuzzy sets theory to deal with the undeterministic factors in financial markets.In addition,in a real investment environment,the investors usually have multiple conflicting and competing objectives to be optimized simultaneously,in the course of investment,investors generally seek the best combination of assets among their investment objectives.Thus,in essence,the portfolio selection problem inherently involves multiple conflicting criteria.At present,the vast majority portfolio selection problems are focused on single objective portfolio selection model,which fails to meet the demand of investors who have multiple investment objectives,and the research about fuzzy multi-objective portfolio selection problems is still at the exploratory stage.Therefore,the main purpose of this paper is to apply the fuzzy set theory,multi-objective optimization principle and multi-objective evolutionary algorithm to study the fuzzy multi-objective portfolio selection problem,and then to establish a new analytical framework for investment decision theory.The main contributions of this dissertation are as follows:1.The main drawbacks of mean-variance model are easy to generate corner solutions and low diversity of the portfolios.To overcome these defects,firstly,we propose a new proportion entropy function as an objective function to generate well-diversified portfolios.Secondly,based on the possibilistic theory,three kinds of multi-objective portfolio selection models are proposed,which are possibilistic mean-variance,mean-varianceShannon-entropy and mean-variance-proportional-entropy portfolio selection models.Thirdly,an orthogonal multi-objective evolutionary algorithm based on space decomposition is designed to solve the model,and the performances of the three portfolio selection models are compared.The results show that the possibilistic mean-variance- proportion-entropy portfolio selection model is more effective than the possibilistic mean-variance and the mean-variance-Shannon entropy models.Finally,the proposed entropy function in this paper shows better performance in measuring the diversity of portfolios.2.In view of the skewed distribution of the return of risky assets,the fuzzy skewness is used to describe the asymmetric distribution of the return of risky assets,and a possibilistic mean-variance skewness multi-objective portfolio selection model is proposed.In order to improve the diversity of the portfolios,the entropy function used as an objective function,and an improved possibilistic mean-variance-skewness portfolio selection model is proposed in multi-objective framework.Then,an improved multi-objective evolutionary algorithm is designed to solve the model,which makes the Pareto-optimal solution obtained by the algorithm own good convergence and diversity.Finally,a fuzzy skewness Sharpe ratio is presented to evaluate the performance of the two multi-objective portfolio selection models.The results show that the mean variance skewness entropy portfolio selection model can obtain more decentralized investment strategies and more efficient portfolio.3.In order to deal with the influence of skewness and kurtosis on the portfolio selection problem,firstly,a possibilistc mean-variance-skewness-kurtosis higher moment portfolio selection model is proposed in multi-objective framework.Secondly,in order to overcome the low diversity of the obtained solution set and the corner solutions for the higher moment portfolio selection models,three kinds possibilistic mean-variance-skewnesskurtosis-entropy multi-objective higher order moment portfolio models are presented by using three different entropy functions.Thirdly,a multi-objective evolutionary algorithm is designed based on space decomposition and crowing distance to solve the proposed multi-objective portfolio selection problems.Finally,a new fuzzy Adjusted Sharpe Ratio is proposed to evaluate the performance of these multi-objective higher order moment portfolio models.The results show that the entropy function,added as the objective function in higher order moment portfolio model,enhances the diversity of the portfolio.In addition,the proportional entropy function proposed in this paper is more effective in measuring the diversity of portfolios.4.The risk measure plays an important role for portfolio selection problems.The lower partial risk(downside risk)measures have been considered to be more in line with investor's attitude towards risk.Therefore,in the lower partial risk framework,the semi-variance and semi-absolute-deviation risk measures are used as a double-risk measures simultaneously,and a possibilistic mean semi-variance semi-absolute deviation multi-objective portfolio selection model is proposed.In order to make the model more realistic,we considered the transaction cost,liquidity and cardinality constrained in the proposed portfolio model.Finally,a multi-objective evolutionary algorithm based on uniform design is designed to solve the proposed portfolio model.According to the experimental results,the optimal number of assets and the corresponding core assets for the proposed portfolio selection model are given.5.For the proposed multi-objective portfolio selection models,several multi-objective evolutionary algorithms are presented to deal with these models,and numerical experiments are carried out on the models and the algorithms.The results verified the applicability of the models and the effectiveness of proposed algorithms. |
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