Research On Multi-period Fuzzy Portfolio Selection Optimization Model And Algorithm

How to reasonably allocate investors’ wealth among different assets based on their owninvetment intention is an extensively concerned problem for extensive financial researchersand asset managers. In real world, investors’ behaviors are usually multi-period. AfterMarkowitz’s single period mean-variance model, numerous researchers have proposed aseries of multi-period portfolio selection models under the framework of probability theory.All these models only consider the random uncertainty associated with financial market andneglect the fuzzy uncertainty on the return of asset. With the widely use of fuzzy set theory,people have realized that they could utilize the fuzzy set theory to handle the uncertainty infinancial markets. Up to now, researches on portfolio seletion in fuzzy environment are mainconcerned on portfolio selection in single period cases, and studies about multi-periodportfolio selection in fuzzy environment are still on exploratory stage. This thesis combinesfuzzy set theory, optimization method and intelligent optimization approaches to study themulti-period portfolio selection problem with fuzzy uncertainty. And then, we try to constructthe framework of multi-period fuzzy portfolio selection theory.The main researches and contributions of this thesis can be summarized as follows:（1）We propose some multi-period portfolio selection models based on possiblistichigher moments with open-loop and closed-loop policies. Meanwhile, we designcorresponding algorithms to solve these proposed models. Since most of traditionalmulti-period portfolio optimization models are open-loop policy models, they usuallyconsider two main factors, namely, return and risk. Few researches have considered theinfluence of higher moments on the multi-period portfolio selection. Actually, numerousstudies have shown that the effect of higher moments on portfolio decision-making cannot beneglected. For this problem, we use possibility theory to investigate it. Under the frameworkof mean-variance, we substitute possbilistic variance by possbilistic semi-variance as riskmeasure and propose two single-objective models with open-loop policies. Then, on the basisof the two models, we consider the influence of skewness and kurtosis on portfoliodecision-making. We characterize the skewness and kurtosis of portfolio by third possiblisitcmoment and fourth possiblisitc moment, respectively. After that, we propose fourmulti-objective portfolio optimizaiton models based on possibilistic higher moments tosimulate investors’ investment behavior. We design an improved genetic algorithm to solvethese proposed model. Meanwhile, numerical examples by collecting real data in Chinesesecurity markets are given to demonstrate the application of the proposed models. Additionally, to make further analysis about the deviation between the real return of securityand its expected return on portfolio decision-making, we propose two multi-period portfoliooptimization models by using dynamic feedback control theory. Besides, comparsion analysisis provided by an application example to highlight the advatages of closed-loop policy modelsover the corresponding open-loop policy models.（2）We construct a possiblistic entropy to measure the diversifcation degree of portfolio.Then, we propose a multi-period diversified portfolio selection model based on possiblisticmean-semivariance-entropy. A genetic simulated annealing algorithm is designed for solution.In traditiondal portfolio selection models, researchers were accustomed to employ theproportion entropy to measure the diversification degree of portfolio. However, usingproportion entropy may lead to an extremely diversified portfolio, which is not an optimalinvestment strategy. To overcome aforementioned shortcomings, we construct a novelpossiblistic entropy to measure the diversification degree of portfolio and then we present apossiblistic mean-semivariance-entropy model with transaction cost. Meantime, we stillconstruct a multi-period portofolio optimization model based on proportion entropy formaking a comparsion analysis. Then, a genetic simulated annealing algorithm is designed forsolving the proposed model. Finally, application examples are given to demonstrate theadvantages of diversified portflio model based on possiblistic entropy over the proportionentropy model.（3）We propose a multi-period portfolio seleciton model by using interval programmingand a multi-period portfolio seleciton model with admissible deviations to investigate themulti-period portfolio optimization problems in emerging markets with information severeshortage and admissible deviations, respectively. Solution algorithms are also given to solvethe proposed models. So far, researches about emerging markets, in which the historicalinformation is severe shortage, are all concerned about single period portfolio selection. Thereare few studies on multi-period portfolio selection. Thus, the purpose of this thesis is to usethe interval programming approach to investigate above-mentioned problem. We propose fourmulti-period portfolio selection models by using interval programming. Then, we transformthe proposed four interval programming models into corresponding crisp form of nonlinearprogramming problems by using the definition of possibility degree, which measures theorder relations of interval numbers. Finally, a feasibility-based particle swarm optimization(PSO) algorithm is designed to for solution. Application examples are also given todemonstrate the application of these models and the effectiveness of the designed algorithm. Besides, to make further analysis investors’ decision-making mind, we also use the fuzzymeasure theory to investigate multi-period portfolio selection problem with admissibledeviations and give an improved differential evolution aglorithm to solve the proposedmodels.（4）We investigate multi-period portfolio selection problem with bankruptcy control byusing credibility theory and propose two multi-period bankruptcy control model based oncredibilitic measure. Meanwhile, we design corresponding hybrid intelligent algorithms tosolve the two proposed models. Until now, few researches have concerned on the multi-periodbankruptcy control problem in fuzzy environment. This thesis uses the credibility theory tostudy above-mentioned problem. The main contents of this topic can be summarized asfollows:（i）Research on multi-period bankrutcy control model with the objective ofmaximizing credibilitic return. Under the framework of mean-variance model, we usecredibility theory to study multi-period fuzzy portfolio selection problem with bankruptcycontrol. We qualify the investment return and risk by credibilitic mean and variance,respectively. Then, we propose a self-finacing bankruptcy control model for multi-periodportfolio seletion with the objective to maximize the credibilitic return. Meanwhile, we designa novel hybrid gentic algorithm with particle swarm algorithm for solution. After that, we givean empirical analysis to illustrate the application of the proposed model and demonstrate theeffectiveness of the designed algorithm.（ii）Researches on bankruptcy control problem basedon credibilitic return-lower side risk-entropy. This thesis extends the aforementioned riskcontrol model with maximizing credibilitic return. We consider the influence of the fuzzyuncertainty associated with the return of asset on portfolio decision-making. We substitutecredibilitic variance with the credibilitic lower side risk as the risk measure of asset andqualify the fuzzy uncertainty on the return of asset by credibilitic entropy. A credibiliticmean-lower side risk-entropy portfolio optimization model with bankruptcy control isproposed. Since the proposed model is a tri-objective optimization problem, we employ fuzzymutli-criteria decision-making theory to transform it into a corresponding single objetiveprogramming problem. A hybrid intelligent algorithm is designed to for solution and anumerical example is given to demonstrate the effectiveness of the designed algorithm.