统计与数据科学学院知识库

       在金融投资领域，投资者将资金分配到不同投资标的，以分散投资风险并获取可观收益。在配置资金之前，确定最优资产配置策略是最为关键的一步。自1952 年 Markowitz 提出量化收益与风险的均值-方差模型以来，国内外学者相继提出各种投资组合模型。这些模型大多是在均值-风险框架下基于不同风险度量方法构建的多目标优化模型，而且没有考虑现实投资中金融资产收益具有的分形特征。因此，本文基于分形视角研究兼顾收益与风险的投资组合优化模型是必要且有意义的。

       本文的主要工作如下：

       (1)考虑金融资产收益具有分形特征，分别从单分形分析结合非对称拉普拉斯分布(Asymmetric Laplacian distribution,ALD)和多重分形分析结合波动函数的角度对投资组合的风险进行研究，进而提出了兼顾收益与风险的R-ALCV-R和R-MF-R 收益-分形风险比模型。

       (2)对传统教与学算法(TLBO)的基本原理进行介绍，加入自适应选择学习算子，从提高算法精度这个角度来对其进行改进，提出改进学习算子的教与学算法(SLTLBO)。运用基准函数对改进后的算法性能进行测试，结果表明，改进后的SLTLBO 算法在收敛精度方面相比于传统的 TLBO 算法更具优势。

       (3)以上证 50 指数的主要成分股为研究对象，分析上海股票市场的分形特征；使用 SLTLBO 算法对本文构建的 R-ALCV-R 和 R-MF-R 收益-分形风险比模型及传统投资组合模型进行求解；通过比较不同调整周期策略下的收益率、标准差、夏普比率及累计收益率，给出最优投资策略。

       实证结果表明，在以年为周期动态调整最优资产配置比例的情况下，本文提出的两种收益-分形风险比模型均优于传统投资组合模型。

       In the field of financial investment, investors allocate funds to different investment targets to spread investment risks and obtain considerable returns. Determining the optimal asset allocation strategy  is the most critical step before allocating funds. Since Markowitz put forward the mean-variance model to quantify returns and risks in1952, scholars at home and abroad have put forward various portfolio modelsone after another. Most of these models are multi-objective optimization models based on different risk measurement methods under the mean-risk framework, and the fractal characteristics of financial asset returns in real investment are not considered. Therefore, it is necessary and meaningful to study the portfolio optimization model based on fractal perspective, which takes into account both returns and risks.

            The main work of this thesis is as follows:

           (1) Considering the fractal characteristics of financial assets returns, the risk of portfolio is studied from the perspectives of single fractal analysis combined with asymmetric Laplacian distribution (ALD) andmulti-fractal analysis combined with fluctuation function, and then R-ALCV-R and R-MF-R return-fractal risk ratio models with both returns and risks are proposed.

       (2) Introduce the basic principle of the traditional teaching and learning algorithm (TLBO), add adaptive selective learning operator, improve it from the point of improving the accuracy of the algorithm, and put forward the improved learning operator teaching and learning algorithm (SLTLBO). The benchmark function is used to test the performance of the improved algorithm. The results show that the improved SLTLBO algorithm has more advantages than the traditional TLBO algorithm in convergence accuracy.

           (3) The fractal characteristics of Shanghai stock market are analyzed by taking the main constituent stocks of the SSE 50 Index as the research object; The SLTLBO algorithm is used to solve the R-ALCV-R and R-MF-R income-fractal risk ratio models and traditional portfolio models constructed in this thesis; By comparing the return rate, standard deviation, Sharp ratio and cumulative return rate under different adjustment cycle strategies, the optimal investment strategy is given.

         The empirical results show that the two income-fractal risk ratio models proposed in this thesis are better than the traditional portfolio model when the optimal asset allocation ratio is dynamically adjusted on an annual basis.