存在融资的模糊决策投资组合模型的研究及应用

摘要

利用应用效果较好的均值-半偏差投资组合模型对存在融资情况的投资组合进行分析研究。将存在融资情况的均值-半偏差模型的收益和风险目标进行模糊化，并构造了使用较多且效果佳的线性隶属度函数μmax(x)和μmin(x)。运用模糊决策理论引进变量μ将模糊环境下存在融资的双目标模型转化为线性的基于模糊决策存在融资的投资组合模型。本模型不仅简化了模型的计算量，同时也将投资者的主观投资意愿表示清楚。最后通过实例说明了模型的实用性和有效性。%The effective mean-semi-deviation portfolio model is used for the analysis of the investment port-folio with financing in this paper. First, the gain obtained by the mean- semi-deviation model with finan-cing and the risks of the goal are described in a fuzzy way by constructing the linear membership functions μmax(x) and μmin(x) , which are widely used. Then, based on fuzzy decision theory, variable ft is intro-duced to transform the bi-objective model with financing under fuzzy environment into a linear portfolio se-lection model with financing. This model not only greatly simplifies the computation, but also clearly de-scribes the subjective investment willingness of the investors. Finally, an example is presented to illustrate the applicability and effectiveness of the proposed model.