Monte Carlo simulation of SDEs using GANs

Abstract Generative adversarial networks (GANs) have shown promising results when applied on partial differential equations and financial time series generation. We investigate if GANs can also be used to approximate one-dimensional It $$\hat{\text {o}}$$ o ^ stochastic (SDEs). propose a scheme that approximates the path-wise conditional distribution of SDEs for large steps. Standard are only able processes in distribution, yielding weak approximation SDE. A GAN architecture is proposed enables strong approximation. inform discriminator this with map between prior input generator corresponding output samples, i.e. we introduce ‘supervised GAN’. compare input-output obtained standard supervised show experimentally may fail provide The trained dataset exact simulation. was tested geometric Brownian motion (GBM) Cox–Ingersoll–Ross (CIR) process. outperformed Euler Milstein schemes error discretisation approximating distribution. demonstrate how give rise non-parsimonious maps sensitive perturbations, which motivates need constraints regularisation generators.