基于可信性理论的动态投资组合模型及决策研究

项目名称： 基于可信性理论的动态投资组合模型及决策研究

项目编号： No.70871011

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 金属学与金属工艺

项目作者： 黄晓霞

作者单位： 北京科技大学

项目金额： 24万元

中文摘要： 本项目研究的是模糊不确定环境下对多种资产进行选择和组合的优化问题，我们较系统地研究了可信性测度和可信性理论在模糊投资组合中的应用，研究了模糊多阶段动态投资组合问题，扩展了基于可信性测度的均值-方差模型，将其扩展应用到多种投资情况下，研究了当投资者不能准确给出待选证券收益的均值和方差，而只能给出一族隶属函数来描述证券收益时的均值-方差模型，研究了自融资条件下存在交易成本的多阶段均值-方差模型，研究了当汇率和待选证券的收益都是不确定时的跨境投资的均值-方差模型；研究了不同投资者对风险的理解，研究了风险的新的数学描述，提出了不确定在险值概念并给出了多阶段均值-不确定在险值模型；此外，我们还进一步研究了可信性测度在投资组合应用中的改进问题，提出了用不确定测度作为基本测度的研究思路，并进行了基于不确定测度的投资组合问题研究，提出了风险指数的概念和均值-风险指数的投资组合模型，此外，我们还将研究成果初步应用到了国际资本预算中，给出了跨国资本预算的均值-机会约束模型。

中文关键词： 模糊动态投资组合；模糊投资组合；可信性理论 ；模糊规划

英文摘要： The project researches on optimal portfolio selection and capital allocation in fuzzy environment based on credibility measure and credibility theory. We have systematically studied the application of credibility theory on fuzzy portfolio selection. The work mainly focused on the extension of traditional Markowitz model to a variety of fuzzy investment environment and proposed fuzzy multi-period self-financed mean-variance models, fuzzy minimax selection models when security returns are only known to be long to a type of fuzzy variable but the exact fuzzy variable cannot be known, and the fuzzy mean-variance international portfolio selection models. We further analyzed quantitative description of risk and proposed the concept of value at risk in uncertainty and developed multi-period uncertain mean-value-at-risk-in-uncertainty models. In addition, we studied the improvement of credibility as the measure of chance of a fuzzy event and proposed to apply uncertainty measure into portfolio selection problems with security returns subject to human estimations. We have proposed the concept of uncertain risk index based on uncertainty measure and proposed mean-risk index model. Furthermore, we have successfully extended the research result obtained in portfolio selection to the area of capital budgeting and proposed a multi-national capital budgeting model.

英文关键词： fuzzy dynamic portfolio selection; fuzzy portfolio selection; credibility theory; fuzzy programming