Adapted time steps explicit scheme for monotone BSDEs

TL;DR

This paper introduces an explicit numerical scheme with adaptive time-steps for monotone BSDEs, ensuring strong stability and convergence, supported by theoretical proofs and numerical experiments.

Contribution

It presents a novel explicit scheme with adaptive time-steps for monotone BSDEs, guaranteeing stability and convergence, which was not previously available.

Findings

The scheme achieves numerical strong stability for monotone BSDEs.

Convergence of the scheme is rigorously proven.

Numerical simulations confirm the theoretical results.

Abstract

We study the numerical strong stability of explicit schemes for the numerical approximation of the solution to a BSDE where the driver has polynomial growth in the primary variable and satisfies a monotone decreasing condition, and we introduce an explicit scheme with adapted time-steps that guarantee numerical strong stability. We then prove the convergence of this scheme and illustrate it with numerical simulations.