不确定变量下的投资组合模型

发布时间：2018-11-27 18:32

【摘要】：投资组合问题即从大量的候选资产中选出一个资产组合能够最好的满足投资者的目标。近年来,随着可信性理论和不确定理论的发展,许多学者开始利用它们来研究投资组合问题。大量的模糊或不确定变量下的投资组合模型被广泛的提出。本文基于可信性理论和不确定理论做了如下的研究工作:1.研究了基于模糊变量间距离的投资组合模型。利用模糊变量间的距离作为衡量模糊投资收益与优先给出的参照收益之间分歧度的测度。用期望反映投资收益,分别用方差、半方差度量投资风险给出两个新的数学模型。最后,几个数值算例被给出,数值结果证明了所提出的方法是有效的。2.研究了考虑投资者风险态度的投资组合模型。用期望来衡量投资收益,分别用方差、半方差及条件约束来反映投资风险,我们提出了三个带有投资者风险态度的投资组合模型,以便于拥有不同风险态度的投资者能够更容易获得有效的最优投资策略。3.研究了不确定变量下的均值-目标半方差投资组合模型。我们给出了不确定变量下的目标半方差风险函数,进一步提出了一个不确定变量下的均值-目标半方差分散模型。此外,为了解决所提出的模型,一个混合智能算法被设计。最后,数值实验的结果表明所提出模型是有效的。
[Abstract]:Portfolio problem is to select a portfolio from a large number of candidate assets to best meet the objectives of investors. In recent years, with the development of credibility theory and uncertainty theory, many scholars began to use them to study portfolio problems. A large number of fuzzy or uncertain variables under the portfolio model has been widely proposed. Based on credibility theory and uncertainty theory, this paper does the following research work: 1. The portfolio model based on the distance between fuzzy variables is studied. The distance between fuzzy variables is used as a measure to measure the divergence between fuzzy investment returns and preferential reference returns. Two new mathematical models are given to measure investment risk by using expectation to reflect investment return and to measure investment risk by variance and semi-variance respectively. Finally, several numerical examples are given and the numerical results show that the proposed method is effective. 2. 2. A portfolio model considering investor's risk attitude is studied. We propose three portfolio models with investor risk attitude, which measure investment return by expectation, reflect investment risk by variance, semi-variance and conditional constraints, respectively. To make it easier for investors with different risk attitudes to obtain an effective and optimal investment strategy. The mean-target semi-variance portfolio model with uncertain variables is studied. We give the risk function of target semi-variance under uncertain variables, and further propose a mean-target semi-variance decentralized model under uncertain variables. In addition, in order to solve the proposed model, a hybrid intelligent algorithm is designed. Finally, the numerical results show that the proposed model is effective.
【学位授予单位】：渤海大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：F832.48

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