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

Abstract

We investigate solving partial integro-differential equations (PIDEs) using unsupervised deep learning in this paper. To price options, assuming underlying processes follow Levy processes, we require to solve PIDEs. In supervised deep learning, pre-calculated labels are used to train neural networks to fit the solution of the PIDE. In an unsupervised deep learning, neural networks are employed as the solution, and the derivatives and the integrals in the PIDE are calculated based on the neural network. By matching the PIDE and its boundary conditions, the neural network gives an accurate solution of the PIDE. Once trained, it would be fast for calculating options values as well as option Greeks.

arXiv comment22 pages, 4 figures

References in corpus (11)

• Adam: A Method for Stochastic Optimization
• Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
• Artificial Neural Networks for Solving Ordinary and Partial Differential Equations
• DGM: A deep learning algorithm for solving partial differential equations
• Solving high-dimensional partial differential equations using deep learning
• Searching for Activation Functions
• Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations
• Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning
• Deep calibration of rough stochastic volatility models
• Deep learning calibration of option pricing models: some pitfalls and solutions
• Deeply Learning Derivatives