In this paper we demonstrate both theoretically as well as numerically that neural networks can detect model-free static arbitrage opportunities whenever the market admits some. Due to the use of neural networks, our method can be applied to financial markets with a high number of traded securities and ensures almost immediate execution of the corresponding trading strategies. To demonstrate its tractability, effectiveness, and robustness we provide examples using real financial data. From a technical point of view, we prove that a single neural network can approximately solve a class of convex semi-infinite programs, which is the key result in order to derive our theoretical results that neural networks can detect model-free static arbitrage strategies whenever the financial market admits such opportunities.

翻译：本文从理论和数值两方面证明，当市场存在无模型静态套利机会时，神经网络能够检测到这些机会。由于采用神经网络，我们的方法可适用于交易证券数量众多的金融市场，并能确保相应交易策略的几乎即时执行。为证明其可操作性、有效性和鲁棒性，我们提供了使用真实金融数据的示例。从技术角度看，我们证明了单个神经网络能够近似求解一类凸半无限规划问题，这一关键结论推导出我们的核心理论结果：当金融市场存在无模型静态套利机会时，神经网络能够检测到这些策略。