# Multistep schemes for solving backward stochastic differential equations on GPU

arXiv: https://arxiv.org/abs/1909.13560 · HTML: https://mlsanity.com/paper/1909.13560/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2019.

## Built on by (most cited first, 2 of 2)

- [A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations](https://mlsanity.com/paper/2404.08456/) (2024)
- [Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations](https://mlsanity.com/paper/2310.03393/) (2023)

## Abstract (arXiv)

The goal of this work is to parallelize the multistep scheme for the numerical approximation of the backward stochastic differential equations (BSDEs) in order to achieve both, a high accuracy and a reduction of the computation time as well. In the multistep scheme the computations at each grid point are independent and this fact motivates us to select massively parallel GPU computing using CUDA. In our investigations we identify performance bottlenecks and apply appropriate optimization techniques for reducing the computation time, using a uniform domain. Finally, some examples with financial applications are provided to demonstrate the achieved acceleration on GPUs.