【作者】 王燕青；

【导师】 唐万生；

【作者基本信息】 天津大学 ， 管理科学与工程， 2004， 博士

【摘要】 金融市场存在着大量的不确定性,表现为随机性和模糊性,在风险资产的投资中则表现为未来收益率的不确定性.本文提出了概率准则及模糊准则下投资组合模型,并给出了相应的求解算法,具体内容如下:首先,针对不同的投资者对获利性的要求不同,无论其预期收益如何,总是希望能找到一投资组合,使实现预期收益率的概率最大,因此提出了概率准则下投资组合模型.即目标函数为实际投资组合的收益率不低于预期水平的概率;而动态投资组合中的目标函数则为每一阶段末的实际收益率不低于预期水平的概率和,或者为最后一阶段中投资组合的收益率不低于预期水平的概率.其次,由于在投资问题中,往往有人的主观判断,不确定性表现为模糊性,本文又提出了模糊准则下投资组合模型.即目标函数为实际投资组合的收益率不低于预期水平的可能性(必要性、可信性);而动态投资组合中的目标函数则为每一阶段末的实际收益率不低于预期水平的可能性(必要性、可信性)之和,或者为在最后一阶段中,其实际投资组合的收益率不低于预期水平的可能性(必要性、可信性).最后,由于概率准则下的目标函数难以给出其确定性等价类,而模糊准则下的目标函数难以给出其清晰等价类,它们均无法用传统的解法进行求解,因此设计出一套基于随机模拟(模糊模拟)的遗传算法和人工神经网络相结合的混合智能算法.即采用随机模拟(模糊模拟)技术来计算目标函数,采用遗传算法进行寻优;而在动态投资组合中,则利用人工神经网络技术来函数逼近上一阶段中的最优策略和最优值函数,参与下一阶段的优化计算.实例证明,给出的混合智能算法具有很好的收敛性和较高的计算效率.更多还原

【Abstract】 Stochastic and fuzzy are two main aspects of the uncertainty in the financialmarket. The uncertainty of securities’ return rate is the case. In this thesis, the modelsof portfolio selection with probability criterion and fuzzy criterion are put forwardrespectively and their hybrid intelligent algorithms are also designed. The concretecontents are as follows:An investor may have a claim for the expected rate of return, and hope to find aset of securities to maximize the probability of his achievement. So the models ofportfolio selection with probability criterion are put forward. The criterion function isthe probability that the return rate of the portfolio is not lower than a given expectedrate. For dynamic portfolio selection, it is the sum of probability that the return rate ofportfolio at the end of each period is not lower than a given one or the probability thatthe terminal return rate of portfolio is not lower than a given one.The financial market is characterized by fuzziness because of an investor’ssubjective judgment. Therefore, the models of portfolio selection with fuzzy criterionare investigated. The criterion function is the possibility (necessity or credibility) thatthe return rate of portfolio is not lower than a given expected rate. For dynamicportfolio selection, it is the sum of possibility (necessity or credibility) that the returnrate of portfolio at the end of each period is not lower than a given one or thepossibility (necessity or credibility) that the terminal return rate of portfolio is notlower than a given one.The models of portfolio selection with probability criterion and fuzzy criterionare no longer solved by the traditional methods since the criterion functions can’t beconverted to their deterministic equivalents and crisp equivalents. Hybrid intelligentalgorithms are designed when stochastic simulation (fuzzy simulation) based geneticalgorithms and artificial neural network are integrated. The criterion functions arecalculated by stochastic simulation (fuzzy simulation) and optimized by geneticalgorithms. During dynamic portfolio selection, the approximate functions of thestrategy and criterion function can be obtained by using artificial neural network tosubstitute for their numerical solutions in the preceding step. Illustrate examples aregiven and the effectiveness of the proposed hybrid intelligent algorithms is shown.更多还原