This study presents an unsupervised machine learning approach for optimizing
Profit and Loss (PnL) in quantitative finance. Our algorithm, akin to an
unsupervised variant of linear regression, maximizes the Sharpe Ratio of PnL
generated from signals constructed linearly from exogenous variables. The
methodology employs a linear relationship between exogenous variables and the
trading signal, with the objective of maximizing the Sharpe Ratio through
parameter optimization. Empirical application on an ETF representing U.S.
Treasury bonds demonstrates the model's effectiveness, supported by
regularization techniques to mitigate overfitting. The study concludes with
potential avenues for further development, including generalized time steps and
enhanced corrective terms.

这项研究提出了一种无监督机器学习方法来优化量化金融中的盈亏（Profit and Loss）。我们的算法类似于无监督线性回归，通过线性组合外生变量构造的信号，最大化盈亏的夏普比率。该方法利用外生变量与交易信号之间的线性关系，通过参数优化来最大化夏普比率。在代表美国国债的 ETF 上的实证应用展示了模型的有效性，并通过正则化技术来减少过拟合。研究总结了进一步发展的潜在方向，包括广义时间步长和增强校正项。