An unsupervised deep learning approach to solving partial integro-differential equations

Abstract

We investigate solving partial integro-differential equations (PIDEs) using unsupervised deep learning. The PIDE is employed for option pricing, when the underlying process is a Lévy process with jumps. The unsupervised deep learning approach employs a neural network as the candidate solution and trains the neural network to satisfy the PIDE. By matching the PIDE and the boundary conditions, the neural network would yield an accurate solution to the PIDE. Unlike supervised learning, this approach does not require any labels for training, where labels are typically option prices as well as Greeks.