Random walk approximation of BSDEs with H{\"o}lder continuous terminal condition

TL;DR

This paper studies the approximation of Markovian BSDE solutions with H{"o}lder continuous terminal conditions using random walks, providing convergence rates and analyzing the solution's PDE properties.

Contribution

It improves existing results by establishing new properties of the second spatial derivative of the PDE solution associated with the BSDE.

Findings

Established L2-convergence rates for the approximation

Analyzed growth and smoothness of the PDE solution u

Proved new properties of the second derivative of u

Abstract

In this paper we consider the random walk approximation of the solution of a Markovian BSDE whose terminal condition is a locally H{\"o}lder continuous function of the Brownian motion. We state the rate of the L 2-convergence of the approximated solution to the true one. The proof relies in part on growth and smoothness properties of the solution u of the associated PDE. Here we improve existing results by showing some properties of the second derivative of u in space.