基于模糊收益率的分散化投资组合调整策略

投资组合选择是量化金融领域的核心问题之一。本文研究模糊环境下考虑交易费用和基数约束的分散化投资组合调整问题。首先，将风险资产的收益率视为模糊变量，通过建立一个模糊收益率拟合模型，确定了各资产收益率的模糊分布。其次，通过提出一个新的分散化测度，建立了模糊均值-下半方差-分散化投资组合调整模型。然后，设计了一个改进的遗传算法对模型进行求解。最后，选取真实的股票数据进行实例分析。结果表明所提出的策略优于传统的投资组合调整策略。

A Diversified Portfolio Selection Strategy Based on Fuzzy Return Rate

Portfolio selection is one of the core issues in the field of quantitative finance. A diversified portfolio selection strategy is proposed by considering transaction cost and cardinality constraint. Firstly, the return rates of risky assets are regarded as fuzzy numbers and a fuzzy return rate fitting model is proposed to determine the fuzzy distribution of the assets’ return rates. Then, a new diversification measure is proposed for the portfolio and a fuzzy mean-semi-variance-diversification portfolio selection model is established. Next, a modified genetic algorithm is designed to solve the proposed models. Finally, an empirical example with real stock data is used to illustrate the proposed strategy. The results show that the proposed strategy performs better than the conventional portfolio selection strategies.