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构建合理的投资组合能够实现资金的有效配置，对于提高收益和降低风险至关重要。随着机器学习方法的蓬勃发展，深度学习和智能优化算法等新兴技术与投资组合的融合正在不断改变传统的投资方式。本文首先基于一种生成式深度学习方法——最小二乘生成对抗网络，模拟证券未来收益的复杂多维场景，从而有效把握资产未来收益的不确定性信息。其次，拓展不确定性场景下投资组合的CVaR及收益率高阶矩的估计方式，以解决复杂多维场景计算下的投资损失控制问题。构建多目标投资组合优化问题，弥补仅考虑预期收益和CVaR而忽略高阶矩风险的不足。最后，引入Tent混沌映射和混合惩罚函数以改进NSGA-Ⅲ，从而求解该高维、高阶矩、非线性问题。实证研究以市场规模大且流动性好的上证50指数成份股构建投资组合，结果表明所构建的新模型在样本外累积收益和夏普比率等评价指标上表现更好。本文提出的投资组合模型有助于提高样本外投资绩效，同时也丰富了目前投资组合方法论研究。
Abstract：Constructing a reasonable portfolio can achieve an effective allocation of funds, which is crucial to improving returns and reducing risks. With the vigorous development of machine learning methods, the combination of new technologies such as deep learning and intelligent algorithms with portfolios is continuously changing the traditional way of portfolio selection. Firstly, this paper simulates a large number of future scenarios of securities return based on a generative deep learning method—least square generative adversarial networks, thereby effectively grasping the uncertainty information of future asset returns. Secondly, the estimation methods of CVaR and higher order moment of the portfolio under uncertainty scenarios are expanded to address the problem of investment loss control under sophisticated multi-dimensional scenario calculations. The multi-objective portfolio optimization problem is constructed,which remedies the shortcoming of only considering the expected returns and CVaR but ignoring the high-order moment risk. Finally, by introducing the Tent chaotic map and the mixed penalty function to improve the NSGA-Ⅲ, this high-dimensional, higher-order moment, and nonlinear problem is solved. The empirical study constructs the investment portfolio with the constituent stocks of SSE 50 Index with large market scale and good liquidity. The results show that the new model constructed in this paper performs better on the cumulative return, Sharpe ratio and other metrics. The proposed model can improve the performance of the portfolio, and enrich the current research on portfolio methodology.
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(1)因篇幅所限，定理1和定理2的证明以附录1展示。
(1)因篇幅所限，INSGA-Ⅲ算法流程图以附图2展示。
(1)国泰安（CSMAR）数据库网址为https://data.csmar.com/。
(2)因篇幅所限，各评价指标计算方法以附录2展示。
(1)M-CVa R模型中的均值和CVa R均由GJR-GARCH(1,1)模型计算得出。除EWM模型外，对照模型均根据历史收益率信息构建优化问题并采用序列最小二乘规划进行求解。
(1)上述所有程序均在搭配AMD锐龙5-5600H六核处理器/3.30GHz,16GB内存和单个英伟达GTX1650显卡的计算机上运行。LSGANs每次滚动生成40只股票未来收益场景的运行时间（GPU）为660.4秒，INSGA-Ⅲ每次滚动构建投资组合的运行时间（CPU）为1136秒（运行10次）。以W=100个交易日为滚动窗口且T=10为调仓周期进行滚动投资，在样本外滚动63次构建投资组合的总运行时长为31.437小时。
(1)股票收益的概率密度预测结果与真实收益对比图以附图3展示。
基本信息:
DOI：10.19343/j.cnki.11-1302/c.2024.12.011
中图分类号:F224;F832.51
引用信息:
[1]王帅,王建州.基于复杂多维场景生成的M-CVaR-高阶矩投资组合研究[J].统计研究,2024,41(12):136-150.DOI:10.19343/j.cnki.11-1302/c.2024.12.011.
基金信息:
国家社会科学基金重大项目“大数据时代雾霾污染经济损失评估及防治对策研究”（17ZDA093）
2024-12-25
2024-12-25