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基于模糊决策理论研究了带有成比例交易费用的证券投资组合优化问题。首先,基于半绝对偏差风险函数和极大极小原则提出了一种新的风险函数-极大极小半绝对偏差风险函数;然后,引入一种非线性隶属函数更加形象地描述了投资者对投资收益和投资风险的满意程度;在此基础上,进一步提出了非线性满意程度的模糊决策投资组合选择模型;最后,针对提出的模型,利用中国证券市场的真实数据给出了数值算例。
Based on the fuzzy decision theory, this paper studies the securities investment portfolio optimization problem with proportional transaction costs. First of all, a new risk function - maximum and minimum semi-absolute deviation risk function is proposed based on the semi-absolute deviation risk function and the maximum and minimum principle. Then, a nonlinear membership function is introduced to describe the investors’ Investment returns and investment risk. On this basis, we further propose a fuzzy decision-making portfolio selection model with nonlinear satisfaction. Finally, a numerical example is given using the real data of China’s securities market for the proposed model.