In order to incorporate the multifractal characteristics of the capital market into the research framework of portfolios and overcome the shortcomings of existing research results that had not considered the existence of multiple fractal fluctuation characteristics and multiple fractal correlation characteristics of asset prices, in this paper, multifractal detrended cross-correlation analysis (MF-DCCA) was embedded into the mean–variance criterion, the Mean-MF-DCCA portfolio model was constructed under the constraints of multiple fractal features, and the analytical solution of the model was given. On this basis, the effectiveness of Mean-MF-DCCA portfolio model was tested using empirical analysis. The results showed that the Mean-MF-DCCA portfolio model was effective, and compared with the mean–variance portfolio model, it is more conducive to investors to construct a sophisticated portfolio under the multiple fluctuation importance degree and multiple time scales, so as to improve their portfolio performance.

为了将资本市场的多重分形特征纳入投资组合的研究框架，并克服现有研究结果的不足，即没有考虑资产价格的多重分形波动特征和多重分形相关特征的存在，本文提出了多重分形将去趋势互相关分析（MF-DCCA）嵌入到均值-方差准则中，在多重分形特征的约束下构建了Mean-MF-DCCA投资组合模型，并给出了模型的解析解。在此基础上，使用经验分析检验了Mean-MF-DCCA投资组合模型的有效性。结果表明，Mean-MF-DCCA投资组合模型是有效的，并且与均值-方差投资组合模型进行了比较，