Stratified regression Monte-Carlo scheme for semilinear PDEs and BSDEs with large scale parallelization on GPUs

TL;DR

This paper introduces a stratified regression Monte Carlo algorithm for solving semilinear PDEs and BSDEs, optimized for large-scale parallelization on GPUs, reducing memory overhead and enhancing computational efficiency.

Contribution

The paper presents a novel stratification method within a Least-Squares Monte Carlo framework enabling efficient GPU parallelization for BSDEs.

Findings

Effective large-scale parallelization on GPUs.

Reduced memory requirements compared to previous methods.

Accurate approximation of BSDE solutions.

Abstract

In this paper, we design a novel algorithm based on Least-Squares Monte Carlo (LSMC) in order to approximate the solution of discrete time Backward Stochastic Differential Equations (BSDEs). Our algorithm allows massive parallelization of the computations on many core processors such as graphics processing units (GPUs). Our approach consists of a novel method of stratification which appears to be crucial for large scale parallelization. In this way, we minimize the exposure to the memory requirements due to the storage of simulations. Indeed, we note the lower memory overhead of the method compared with previous works.