Rate of convergence for the discrete-time approximation of reflected BSDEs arising in switching problems

TL;DR

This paper establishes improved convergence rates for discrete-time approximations of multidimensional obliquely reflected backward stochastic differential equations (BSDEs) used in switching problems, under Lipschitz conditions.

Contribution

It provides new convergence results with explicit rates, enhancing previous findings for the approximation of reflected BSDEs in switching models.

Findings

Improved convergence rates for discrete-time schemes.

Applicability under Lipschitz generator conditions.

Extension of previous approximation results.

Abstract

In this paper, we prove new convergence results improving the ones by Chassagneux, Elie and Kharroubi [Ann. Appl. Probab. 22 (2012) 971--1007] for the discrete-time approximation of multidimensional obliquely reflected BSDEs. These BSDEs, arising in the study of switching problems, were considered by Hu and Tang [Probab. Theory Related Fields 147 (2010) 89--121] and generalized by Hamad\`ene and Zhang [Stochastic Process. Appl. 120 (2010) 403--426] and Chassagneux, Elie and Kharroubi [Electron. Commun. Probab. 16 (2011) 120--128]. Our main result is a rate of convergence obtained in the Lipschitz setting and under the same structural conditions on the generator as the one required for the existence and uniqueness of a solution to the obliquely reflected BSDE.