This article introduces the groundbreaking concept of the financial differential machine learning algorithm through a rigorous mathematical framework. Diverging from existing literature on financial machine learning, the work highlights the profound implications of theoretical assumptions within financial models on the construction of machine learning algorithms. This endeavour is particularly timely as the finance landscape witnesses a surge in interest towards data-driven models for the valuation and hedging of derivative products. Notably, the predictive capabilities of neural networks have garnered substantial attention in both academic research and practical financial applications. The approach offers a unified theoretical foundation that facilitates comprehensive comparisons, both at a theoretical level and in experimental outcomes. Importantly, this theoretical grounding lends substantial weight to the experimental results, affirming the differential machine learning method's optimality within the prevailing context. By anchoring the insights in rigorous mathematics, the article bridges the gap between abstract financial concepts and practical algorithmic implementations.

翻译：本文通过严谨的数学框架，阐释了金融微分机器学习算法的开创性概念。与现有金融机器学习文献不同，本研究着重强调了金融模型中的理论假设对机器学习算法构建产生的深远影响。在当前金融领域对数据驱动的衍生品估值与对冲模型兴趣激增的背景下，该研究具有特别的时效性。值得注意的是，神经网络的预测能力已在学术研究和金融实务中引发广泛关注。本方法构建的统一理论框架，既支持理论层面的全面比较，也适用于实验结果的系统性分析。尤为重要的是，这种理论根基赋予实验结果显著的可信度，证实了微分机器学习方法在当下情境中的最优性。通过将研究洞见锚定于严谨数学基础，本文弥合了抽象金融概念与具体算法实现之间的鸿沟。