Multistep schemes for solving backward stochastic differential equations on GPU

TL;DR

This paper develops a GPU-accelerated multistep numerical scheme for solving backward stochastic differential equations, significantly reducing computation time while maintaining high accuracy, with applications demonstrated in finance.

Contribution

It introduces a parallel GPU implementation of multistep schemes for BSDEs, optimizing performance and demonstrating practical acceleration in financial models.

Findings

Significant reduction in computation time on GPU

High accuracy maintained in numerical solutions

Effective optimization techniques applied

Abstract

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.