导　　师： 庄新田

学科专业： 1201

授予学位： 博士

作　　者： ;

机构地区： 东北大学

摘　　要： 投资组合/(Portfolio/)决策研究的核心问题是研究如何把有限资金合理的分配到不同的资产中,以达到分散风险并确保投资收益的目的。而证券投资规划从本质上来说,就是在不确定性的投资环境中,以现代投资组合理论为研究基础,通过建立模拟实际投资情况的数学规划模型,在综合平衡投资收益和投资风险等相关因素的条件下,构造出投资决策分析框架,求解出最优投资决策的研究方法。Markowitz的均值-方差模型就是利用概率论的相关理论度量证券市场的不确定性,在投资组合理论的基本框架下,构造出既定投资收益条件下,最小化投资风险或者是既定投资风险条件下,最大化投资收益的证券投资规划模型。 然而,证券市场中存在着两种不确定性事件：随机不确定性事件和模糊不确定性事件,这样,证券投资规划可以相应的分为度量随机不确定性事件的证券投资规划模型和度量模糊不确定性事件的证券投资规划模型。建立在概率论基础上的均值-方差模型仅考虑了证券市场的随机不确定性,却忽视了模糊不确定性对证券选择的影响,而证券市场中的不确定性事件更多的表现为模糊不确定性事件,模糊不确定性是证券市场固有的本质特征,构建模糊不确定性环境下的证券投资规划模型更加符合实际的投资情况。 本研究立足于我国的实际情况,充分利用定量和定性的知识相结合的办法,利用专家的知识和经验,在深入挖掘证券市场上模糊特性的基础上,综合利用模糊理论和最优化方法来研究证券投资组合的决策问题,为我国的投资实践提供行之有效的决策意见。本研究主要关注以下几个方面： /(1/)模糊环境下投资规划的构建和应用性研究。在模糊不确定环境下,构建出证券投资选择规划,并给出相应地优化求解方法,研究模糊投资规划在投资决策实践中的决策效果,并且在研究单期模糊投资规划构建和优化求解的基础上,研究多期模糊投资规划在证券选择方面的投资决策效果。 /(2/)模糊环境下投资规划的有效性研究。以模糊AR时间序列预测的投资组合未来的收益状况代替样本期望值来度量投资收益,在模糊决策的理论框架下,将绝对偏差度量的投资风险调整为模糊松弛约束,建立目标函数为梯形模糊数的投资收益,风险约束为模糊松弛约束的模糊投资规划,将模糊环境下所求得的有效性前沿和随机环境下的有效性前沿进行比较分析,研究模糊环境下投资规划的有效性以及模糊投资规划比随机投资规划的优越性。 /(3/)模糊环境下二目标梯形模糊数投资规划研究。以模糊时间序列预测投资收益为基础,建立证券价格为梯形模糊数的预测模型,以预测值和购买价格的比值衡量投资收益,以预测收益低于期望值的半绝对偏差度量投资风险,建立了二目标投资规划模型,在充分利用证券市场开盘价、收盘价、最高价和最低价四个价格,在模拟出证券价格的梯形模糊数的基础上,采用折衷规划的方法进行优化求解,利用我国上证50指数的真实数据进行实证检验分析,并与概率框架下的均值-绝对偏差模型的投资组合效果进行比较。 /(4/)模糊环境下二目标区间数投资规划决策研究。采用S型隶属函数描述投资收益为投资者带来的满意度水平,并利用模糊逻辑关系预测未来的满意度水平,构建了模糊目标为区间收益和区间风险的二目标区间数投资规划,利用我国上证180成分指数的真实数据进行实证检验分析。 /(5/)模糊环境下多期投资组合优化研究。将模糊单期规划拓展为多期投资组合,利用解释变量为三角形模糊数的模糊AR模型预测未来的多期投资收益,三角形模糊数的方差和协方差度量投资风险,构建出多期投资规划模型,利用含遗传交叉变异因子的粒子群智能优化算法优化求解,并利用我国深圳证券市场的真实数据进行实证检验。 /(6/)基于两步模糊机会规划的多期决策研究。考虑采用模糊变量为对称三角形模糊数的模糊AR模型预测投资收益,以模糊收益中值的协方差度量投资风险,并将市场的流动性因素纳入投资决策框架,利用模糊数的清晰化公式,将预测的模糊收益转化为清晰化的投资收益,在单期两步模糊机会规划的基础上,构建出模糊多期规划寻求投资收益和投资风险的Pareto解,在动态规划分析框架下,采用含遗传交叉变异因子的粒子群算法求解,并利用我国上证50指数的真实数据进行实证检验。 /(7/)模糊环境下基于情景树多期层次资产配置研究。利用模糊层次分析法,将金融资产中的基本面因素纳入投资分析框架,采用因素变量之间的绝对偏差和相对偏差,构造出模糊判断矩阵,利用所获得的三角形模糊收益综合评价值和模糊风险收益综合评价值,构建出模糊环境下的单期资产配置模型,在情景树的多期框架下,利用市场状态之间的模糊逻辑关系出现的概率,计算相应的贝叶斯概率,将单期模糊投资规划拓展为多期模糊资产配置模型,利用我国沪深300行业指数的真实数据进行实证检验分析。 最后,总结了本文的主要研究内容和结论,并指出了本文研究的局限性和进一步研究的方向。 The core question of the portfolio's decision-making research is to study how to distribute the limiting funds to the different assets in order to achieve the goal which to spread the loss and to ensure the earnings. And in essence, based on the research of the modern portfolio theory, the portfolio investment programming is the research method in the uncertainty environment which to establish the mathematic programming model which can simulate the actual investment complexions, and on the condition of the synthetical balance of the correlative factors, such as, the investment return and the investment risk, to construct the analytic framework of the investment decision, then solve the optimal investment decision. Using the correlative theories of the probability to measure the uncertainty of the security market, and under the basal analytic framework of the modern portfolio theary, Markowitz's mean-variance model is the security programming model which minimize the investment risk on the condition of the certain investment return, or maximize the invesetment retun on the condition of the certain investment risk. However, there are two uncertainty events in the security market: the stochastic uncertainty events and the fuzzy uncertainty events, then the security investment programming can correspondingly be classified the security investment programming model measuring the stochastic uncertainty events and the security investment programming model measuring the fuzzy uncertainty events. Based on the probability theory, mean-variance model only considers the stochastic uncertainty of the security market, while ignores the impact of the fuzzy uncertainty. The uncertainty of the security market is showed more fuzzy uncertainty. The fuzzy uncertainty is the intrinsic and essence characteristic of the security market, establishing the security portfolio programming under the fuzzy uncertainty environment will be more suitable the actual investment decision. Based on the actual situation of our country, by making fully use of the approach which to combine the quantitative and qualitative knowledge, and using the knowledge and experience of the expert, and on the basis of the in-depth digging the fuzzy characteristics of the security market, this study is to research the selectable question of the security investment portfolio by synthetically using the fuzzy theory and optimal method in order to give the effective decision-making advice for the investment practice of our country. The main concern of this study is following aspects: /(1/) The constructing and applied research of the portfolio in the fuzzy environment. Under the fuzzy uncertainty environment, I have constructed the portfolio programming, and gived the optimal and solving methods correspondingly, then studied the decision-making impact of the fuzzy portfolio programming in the investment decision-making practice, and then based on the construction and the optimal solution of the single-period portfolio programming, I have studied the investment decision-making impact of the multi-period fuzzy portfolio programming for the choices of the securities. /(2/) The portfolio validity research in the fuzzy environment. The future return states of the portfolio forecasted by the fuzzy AR model is taken the place of the sample expectation to measure the investment return, and under the framework of the fuzzy decision-making theory, the investment risk measured by the absolute deviation is adjusted by the fuzzy relaxation constraint, and I construct a fuzzy investment programming which the goal function is the investment return of the trapezoidal fuzzy number and the risk constraint is the fuzzy relaxation constraint, compare and analyze the effective frontier of the fuzzy environment and the stochastic environment, and study the validity of the investment programming under the fuzzy environment and the superiority of the compare between the fuzzy portfolio programming and the stochastic portfolio programming. /(3/) The investment programming research of the two-goal trapezoid fuzzy number under the fuzzy environment. I establish the predicting model which the security price is the trapezoidal fuzzy numbers based on the prediction of the fuzzy time series, and measuring the investment return by the ratio of the predicting value and measuring the purchasing price and the investment risk by the semi-absolute deviation which the predicting value is below to the expectation, I construct the two-goal programming, and solve the programming to obtain the optimal solution with the method of the compromise programming based on simulating the trapezoid fuzzy number of the security price by fully using the open price, the close price, the highest price and the lowest price of the security market, then empirically analyze the perform of the fuzzy model with the actual data of the SSE50, and then compare the portfolio perform with the mean-absolute deviation model under the probability framework. /(4/) The portfolio decision-making research of the two-goal interval number under the fuzzy environment. I use the S-type membership to describe the satisfaction degree level of the investment return, and make use of the fuzzy logic relationship to forecast the future satisfaction degree level, then establish the two-goal interval number investment programming which the fuzzy goal is the interval return and the interval risk, and then empirically analyze this fuzzy programming with the actual data of the SSE180. /(5/) The multi-period portfolio optimization research under the fuzzy environment. I spread the fuzzy single programming into the multi-period portfolio, and use the fuzzy AR model that the fuzzy variables are the triangular fuzzy number to predict the future multi-period investment returns, then measure the investment risk with the variance and covariance of the triangular fuzzy number, and then construct the multi-period portfolio model, and solve the optimal solution by using the PSO algorithm with the factor of the genetic cross and the genetic variation, at last, empirically analyze this programming with the actual data of the Shenzhen Security Market. /(6/) The multi-period decision-making research based on the two-step fuzzy chance programming. I predict the investment return by using the fuzzy AR model which the fuzzy variables are the symmetric triangular fuzzy number, and measure the investment risk by the covariance of the fuzzy return middle-value, then introduce the market liquidity into the investment decision-making framework, and then change the predictive fuzzy return to the clear investment return by using the clear formula of the fuzzy number, and based on the establishment the single two-step fuzzy chance programming, I establish a two-stage chance programming in order to obtain the Pareto solution of the investment return and the investment risk, then use the PSO algorithm with the factor of the genetic cross and the genetic variation to solve the optimal solution under the framework of the dynamic programming, and then empirically analyze this programming with the actual data of the SSE.50. /(7/) The multi-period fuzzy AHP asset allocation research based on the scenarios tree under the fuzzy environment. Using the fuzzy AHP method, I introduce the fundamental factors of the financial asset into the framework of the investment analysis, and use the absolute deviation and the relative deviation between the factor variables, then construct the fuzzy judgment matrix, then based on the synthetic evaluate value of the triangular fuzzy return and the synthetic evaluate value of the triangular fuzzy risk, establish the single asset allocation under fuzzy environment, and then with the multi-period framework of the scenarios tree model and the probability appeared the fuzzy logic relationship between the market states, calculate the corresponding Bayesian probability, then extend the single fuzzy investment programming into the multi-period fuzzy asset allocation model, and then empirically analyze the programming with the actual data of the SHSZ300Industry Index. Finally, the main contents and results of our research in this dissertation are summarized as well as future research directions.

关 键 词： 投资规划 模糊数 模糊时间序列 隶属函数 多期规划 资产配置

分 类 号： [F832.51 F224]

领　　域： [经济管理] [经济管理]