Discrete-time approximation of multidimensional BSDEs with oblique reflections
Abstract
In this paper, we study the discrete-time approximation of multidimensional reflected BSDEs of the type of those presented 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]. In comparison to the penalizing approach followed by Hamad\`{e}ne and Jeanblanc [Math. Oper. Res. 32 (2007) 182-192] or Elie and Kharroubi [Statist. Probab. Lett. 80 (2010) 1388-1396], we study a more natural scheme based on oblique projections. We provide a control on the error of the algorithm by introducing and studying the notion of multidimensional discretely reflected BSDE. In the particular case where the driver does not depend on the variable , the error on the grid points is of order , .
Keywords
Cite
@article{arxiv.1210.1407,
title = {Discrete-time approximation of multidimensional BSDEs with oblique reflections},
author = {Jean-Francois Chassagneux and Romuald Elie and Idris Kharroubi},
journal= {arXiv preprint arXiv:1210.1407},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/11-AAP771 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)