We introduce a novel and highly tractable supervised learning approach based on neural networks that can be applied for the computation of model-free price bounds of, potentially high-dimensional, financial derivatives and for the determination of optimal hedging strategies attaining these bounds. In particular, our methodology allows to train a single neural network offline and then to use it online for the fast determination of model-free price bounds of a whole class of financial derivatives with current market data. We show the applicability of this approach and highlight its accuracy in several examples involving real market data. Further, we show how a neural network can be trained to solve martingale optimal transport problems involving fixed marginal distributions instead of financial market data.
翻译:我们采用了基于神经网络的新颖的、高度可移植的、监督监督的学习方法,该方法可用于计算潜在的高维金融衍生物的无模式价格界限和确定达到这些界限的最佳套期保值战略。 特别是,我们的方法允许对单一神经网络进行离线培训,然后在网上使用,以快速确定具有当前市场数据的一整类金融衍生物的无模式价格界限。 我们展示了这一方法的适用性,并在涉及实际市场数据的几个例子中强调了其准确性。 此外,我们展示了如何对神经网络进行培训,以解决涉及固定边际分配而非金融市场数据的最佳运输问题。