We propose a new methodology for pricing options on flow forwards by applying infinite-dimensional neural networks. We recast the pricing problem as an optimisation problem in a Hilbert space of real-valued functions on the positive real line, which is the state space for the term structure dynamics. This optimisation problem is solved by using a feedforward neural network architecture designed for approximating continuous functions on the state space. The proposed neural network is built upon the basis of the Hilbert space. We provide case studies that show its numerical efficiency, with superior performance over that of a classical neural network trained on sampling the term structure curves.

我们提出了一种通过应用无限维神经网络对远期期权进行定价的新方法。我们将定价问题重新定义为正实数线上实值函数希尔伯特空间中的优化问题，这是期限结构动态的状态空间。该优化问题通过使用前馈神经网络架构来解决，该架构设计用于逼近状态空间上的连续函数。所提出的神经网络是建立在希尔伯特空间的基础上的。我们提供的案例研究显示了其数值效率，其性能优于经过采样期限结构曲线训练的经典神经网络。