# Deep Signature FBSDE Algorithm

arXiv: https://arxiv.org/abs/2108.10504 · HTML: https://mlsanity.com/paper/2108.10504/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 40 references that are in the map.
- First posted on arXiv 24 Aug 2021.

## Builds on (most cited first, 10 of 10)

- [Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations](https://mlsanity.com/paper/1706.04702/) (2017)
- [Kernels for sequentially ordered data](https://mlsanity.com/paper/1601.08169/) (2016)
- [Deep Signature Transforms](https://mlsanity.com/paper/1905.08494/) (2019)
- [Signature moments to characterize laws of stochastic processes](https://mlsanity.com/paper/1810.10971/) (2018)
- [The iisignature library: efficient calculation of iterated-integral signatures and log signatures](https://mlsanity.com/paper/1802.08252/) (2018)
- [Deep Learning Methods for Mean Field Control Problems with Delay](https://mlsanity.com/paper/1905.00358/) (2019)
- [Learning stochastic differential equations using RNN with log signature features](https://mlsanity.com/paper/1908.08286/) (2019)
- [PDGM: a Neural Network Approach to Solve Path-Dependent Partial Differential Equations](https://mlsanity.com/paper/2003.02035/) (2020)
- [Convolutional Signature for Sequential Data](https://mlsanity.com/paper/2009.06719/) (2020)
- [Good Deal Hedging and Valuation under Combined Uncertainty about Drift and Volatility](https://mlsanity.com/paper/1704.02505/) (2017)

## Built on by (most cited first, 4 of 4)

- [Deep Signature Algorithm for Multi-dimensional Path-Dependent Options](https://mlsanity.com/paper/2211.11691/) (2022)
- [A deep learning approach to the probabilistic numerical solution of path-dependent partial differential equations](https://mlsanity.com/paper/2209.15010/) (2022)
- [A Deep Learning-Based Method for Fully Coupled Non-Markovian FBSDEs with Applications](https://mlsanity.com/paper/2511.08735/) (2025)
- [Branched Signature Kernel Solvers for ODEs with rough Single-Trajectory signals](https://mlsanity.com/paper/2605.25826/) (2026)

## Abstract (arXiv)

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.