用神经网络非线性压缩协方差矩阵，降低投资组合风险。
Neural Nonlinear Shrinkage of Covariance Matrices for Minimum Variance Portfolio Optimization
- 基于LW估计器分解特征值与特征向量，用轻量Transformer学习非线性收缩函数。
- 在S&P500数据上，新方法出样本真实风险持续低于基准模型。
- 适合量化金融、资产配置研究者，尤其关注风险最小化场景。
本文提出一种基于神经网络的协方差矩阵非线性收缩估计方法，用于最小方差投资组合优化。该方法融合统计估计与机器学习，从Ledoit-Wolf（LW）收缩估计器出发，将协方差矩阵分解为特征值与特征向量，并采用轻量级Transformer神经网络学习非线性特征值收缩函数。模型以投资组合风险为损失函数进行训练，所得到的精度矩阵（即协方差矩阵的逆）直接优化风险最小化目标。通过条件化样本数量与维度比，该方法在不同样本规模和资产池中均保持可扩展性。在标准普尔500指数股票日收益率数据上的实证结果表明，所提方法在出样本真实风险上持续优于基准方法，验证了将结构化统计模型与数据驱动学习结合的潜力。
原文摘要 · Abstract (English)
This paper introduces a neural network-based nonlinear shrinkage estimator of covariance matrices for the purpose of minimum variance portfolio optimization. It is a hybrid approach that integrates statistical estimation with machine learning. Starting from the Ledoit-Wolf (LW) shrinkage estimator, we decompose the LW covariance matrix into its eigenvalues and eigenvectors, and apply a lightweight transformer-based neural network to learn a nonlinear eigenvalue shrinkage function. Trained with portfolio risk as the loss function, the resulting precision matrix (the inverse covariance matrix) estimator directly targets portfolio risk minimization. By conditioning on the sample-to-dimension ratio, the approach remains scalable across different sample sizes and asset universes. Empirical results on stock daily returns from Standard & Poor's 500 Index (S&P500) demonstrate that the proposed method consistently achieves lower out-of-sample realized risk than benchmark approaches. This highlights the promise of integrating structural statistical models with data-driven learning.
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