Path regularity and explicit convergence rate for BSDE with truncated quadratic growth

TL;DR

This paper investigates the path regularity and convergence rates of solutions to quadratic growth backward stochastic differential equations (qgBSDE), extending existing theorems and providing explicit numerical convergence results.

Contribution

It extends Zhang's path regularity theorem to quadratic growth BSDEs and provides explicit convergence rates for truncated solutions, advancing numerical methods for qgBSDE.

Findings

Extended Zhang's path regularity theorem to qgBSDEs

Derived explicit convergence rates for truncated solutions

Proved second order Malliavin differentiability for qgBSDEs

Abstract

We consider backward stochastic differential equations with drivers of quadratic growth (qgBSDE). We prove several statements concerning path regularity and stochastic smoothness of the solution processes of the qgBSDE, in particular we prove an extension of Zhang's path regularity theorem to the quadratic growth setting. We give explicit convergence rates for the difference between the solution of a qgBSDE and its truncation, filling an important gap in numerics for qgBSDE. We give an alternative proof of second order Malliavin differentiability for BSDE with drivers that are Lipschitz continuous (and differentiable), and then derive an analogous result for qgBSDE.