Deep Signature FBSDE Algorithm

TL;DR

This paper introduces a deep signature/log-signature FBSDE algorithm that enhances the efficiency and accuracy of solving complex forward-backward stochastic differential equations with path dependence, applicable to various financial and stochastic models.

Contribution

The paper presents a novel deep signature/log-signature transformation integrated with RNNs for faster, more accurate solutions to FBSDEs, extending to high-dimensional, path-dependent problems.

Findings

Shorter training times compared to existing methods

Improved accuracy in solving FBSDEs

Extended applicability to high-frequency, path-dependent models

Abstract

We propose a deep signature/log-signature FBSDE algorithm to solve forward-backward stochastic differential equations (FBSDEs) with state and path dependent features. By incorporating the deep signature/log-signature transformation into the recurrent neural network (RNN) model, our algorithm shortens the training time, improves the accuracy, and extends the time horizon comparing to methods in the existing literature. Moreover, our algorithms can be applied to a wide range of applications such as state and path dependent option pricing involving high-frequency data, model ambiguity, and stochastic games, which are linked to parabolic partial differential equations (PDEs), and path-dependent PDEs (PPDEs). Lastly, we also derive the convergence analysis of the deep signature/log-signature FBSDE algorithm.