On the wavelets-based SWIFT method for backward stochastic differential equations

TL;DR

This paper introduces a wavelet-based numerical algorithm for backward stochastic differential equations that combines Fourier methods with wavelet simplicity, enhanced by boundary error mitigation techniques, and validated through numerical experiments.

Contribution

It presents a novel wavelet-based SWIFT method for BSDEs, integrating Fourier and wavelet approaches with boundary error correction, improving accuracy and implementation simplicity.

Findings

The method achieves high accuracy in numerical experiments.

Boundary error mitigation improves approximation near edges.

The algorithm is easy to implement and effective.

Abstract

We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based formula, resulting in an algorithm that is both accurate and easy to implement. Furthermore, we mitigate the problem of errors near the computation boundaries by means of an antireflective boundary technique, giving an improved approximation. We test our algorithm with different numerical experiments.