We present convincing empirical results on the application of Randomized Signature Methods for non-linear, non-parametric drift estimation for a multi-variate financial market. Even though drift estimation is notoriously ill defined due to small signal to noise ratio, one can still try to learn optimal non-linear maps from data to future returns for the purposes of portfolio optimization. Randomized Signatures, in contrast to classical signatures, allow for high dimensional market dimension and provide features on the same scale. We do not contribute to the theory of Randomized Signatures here, but rather present our empirical findings on portfolio selection in real world settings including real market data and transaction costs.

我们通过实证研究随机签名方法在多变量金融市场的非线性、非参数漂移估计中的应用，得出令人信服的结果。尽管由于信号噪声比小而导致漂移估计非常不确定，但我们仍然可以尝试从数据中学习到未来回报的最佳非线性映射，以进行投资组合优化。与传统签名方法相比，随机签名方法允许高维市场维度，并提供相同尺度的特征。在这里，我们不对随机签名方法的理论做出贡献，而是介绍我们在真实世界中使用真实市场数据和交易成本进行投资组合选择的经验发现。

最优投资组合选择中的随机签名方法