Numerical simulation of BSDEs with drivers of quadratic growth

TL;DR

This paper develops a new numerical scheme for solving Markovian BSDEs with quadratic growth drivers, providing explicit convergence rates and bounds on the process Z.

Contribution

It introduces a novel non-uniform time discretization scheme for quadratic BSDEs with proven convergence rates and process bounds.

Findings

Established bounds on the process Z.

Proposed a new time discretization scheme.

Derived explicit convergence rates.

Abstract

This article deals with the numerical resolution of Markovian backward stochastic differential equations (BSDEs) with drivers of quadratic growth with respect to $z$ and bounded terminal conditions. We first show some bound estimates on the process $Z$ and we specify the Zhang's path regularity theorem. Then we give a new time discretization scheme with a non uniform time net for such BSDEs and we obtain an explicit convergence rate for this scheme.