Rate of convergence for the discrete-time approximation of reflected BSDEs arising in switching problems
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.
Keywords
Cite
@article{arxiv.1602.00015,
title = {Rate of convergence for the discrete-time approximation of reflected BSDEs arising in switching problems},
author = {Jean-François Chassagneux and Adrien Richou},
journal= {arXiv preprint arXiv:1602.00015},
year = {2018}
}
Comments
Some errors are corrected. In particular, the representation for the scheme given by Proposition 3.3 was modified