# A deep solver for BSDEs with jumps

arXiv: https://arxiv.org/abs/2211.04349 · HTML: https://mlsanity.com/paper/2211.04349/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2022.

## Built on by (most cited first, 9 of 9)

- [Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs](https://mlsanity.com/paper/2405.05192/) (2024)
- [Temporal Difference Learning for High-Dimensional PIDEs with Jumps](https://mlsanity.com/paper/2307.02766/) (2023)
- [A deep implicit-explicit minimizing movement method for option pricing in jump-diffusion models](https://mlsanity.com/paper/2401.06740/) (2024)
- [A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations](https://mlsanity.com/paper/2404.08456/) (2024)
- [Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in Lp-sense](https://mlsanity.com/paper/2409.20431/) (2024)
- [A Deep Learning Analysis of Climate Change, Innovation, and Uncertainty](https://mlsanity.com/paper/2310.13200/) (2023)
- [A deep solver for backward stochastic Volterra integral equations](https://mlsanity.com/paper/2505.18297/) (2025)
- [INEUS: Iterative Neural Solver for High-Dimensional PIDEs](https://mlsanity.com/paper/2605.06281/) (2026)
- [Deep Learning for Reflected BSDEs: Regularization and Error Analysis](https://mlsanity.com/paper/2609.05434/) (2026)

## Abstract (arXiv)

The aim of this work is to propose an extension of the deep solver by Han, Jentzen, E (2018) to the case of forward backward stochastic differential equations (FBSDEs) with jumps. As in the aforementioned solver, starting from a discretized version of the FBSDE and parametrizing the (high dimensional) control processes by means of a family of artificial neural networks (ANNs), the FBSDE is viewed as a model-based reinforcement learning problem and the ANN parameters are fitted so as to minimize a prescribed loss function. We take into account both finite and infinite jump activity by introducing, in the latter case, an approximation with finitely many jumps of the forward process. We successfully apply our algorithm to option pricing problems in low and high dimension and discuss the applicability in the context of counterparty credit risk.