# Deep Signature Algorithm for Multi-dimensional Path-Dependent Options

arXiv: https://arxiv.org/abs/2211.11691 · HTML: https://mlsanity.com/paper/2211.11691/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 50 references that are in the map.
- First posted on arXiv 21 Nov 2022.

## Builds on (most cited first, 11 of 11)

- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Deep Signature Transforms](https://mlsanity.com/paper/1905.08494/) (2019)
- [Convergence of the Deep BSDE Method for Coupled FBSDEs](https://mlsanity.com/paper/1811.01165/) (2018)
- [Optimal Stopping via Randomized Neural Networks](https://mlsanity.com/paper/2104.13669/) (2021)
- [Solving high-dimensional optimal stopping problems using deep learning](https://mlsanity.com/paper/1908.01602/) (2019)
- [Convergence of the Backward Deep BSDE Method with Applications to Optimal Stopping Problems](https://mlsanity.com/paper/2210.04118/) (2022)
- [Deep neural network expressivity for optimal stopping problems](https://mlsanity.com/paper/2210.10443/) (2022)
- [Deep BSDE-ML Learning and Its Application to Model-Free Optimal Control](https://mlsanity.com/paper/2201.01318/) (2022)
- [Deep Signature FBSDE Algorithm](https://mlsanity.com/paper/2108.10504/) (2021)
- [A neural network approach to high-dimensional optimal switching problems with jumps in energy markets](https://mlsanity.com/paper/2210.03045/) (2022)

## Built on by (most cited first, 6 of 6)

- [Recent Developments in Machine Learning Methods for Stochastic Control and Games](https://mlsanity.com/paper/2303.10257/) (2023)
- [Deep Neural Operator Learning for Probabilistic Models](https://mlsanity.com/paper/2511.07235/) (2025)
- [Global universal approximation with Brownian signatures](https://mlsanity.com/paper/2512.16396/) (2025)
- [Branched Signature Kernel Solvers for ODEs with rough Single-Trajectory signals](https://mlsanity.com/paper/2605.25826/) (2026)
- [Forward Trajectory Steering for Hamilton-Jacobi Reachability Analysis](https://mlsanity.com/paper/2608.11480/) (2026)
- [Deep Learning for Reflected BSDEs: Regularization and Error Analysis](https://mlsanity.com/paper/2609.05434/) (2026)

## Abstract (arXiv)

In this work, we study the deep signature algorithms for path-dependent options. We extend the backward scheme in [Hur'e-Pham-Warin. Mathematics of Computation 89, no. 324 (2020)] for state-dependent FBSDEs with reflections to path-dependent FBSDEs with reflections, by adding the signature layer to the backward scheme. Our algorithm applies to both European and American type option pricing problems while the payoff function depends on the whole paths of the underlying forward stock process. We prove the convergence analysis of our numerical algorithm with explicit dependence on the truncation order of the signature and the neural network approximation errors. Numerical examples for the algorithm are provided including: Amerasian option under the Black-Scholes model, American option with a path-dependent geometric mean payoff function, and the Shiryaev's optimal stopping problem.