Discrete-time Approximation of Multidimensional BSDEs with oblique reflections

Chassagneux, Jean-François; Kharroubi, Idris; Elie, Romuald

Chassagneux, Jean-François; Kharroubi, Idris; Elie, Romuald (2012), Discrete-time Approximation of Multidimensional BSDEs with oblique reflections, The Annals of Applied Probability, 22, 3, p. 971-1007. http://dx.doi.org/10.1214/11-AAP771

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00475628/fr/

Date

2012

Journal name

The Annals of Applied Probability

Volume

Number

Publisher

Institute of Mathematical Statistics

Pages

971-1007

Abstract (EN)

In this paper, we study the discrete-time approximation of multi-dimensional reflected BSDEs of the type of those presented by Hu and Tang and generalized by Hamadène and Zhang. In comparison to the penalizing approach followed by Hamadene and Jeanblanc or Elie and Kharroubi, 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 $Z$, the error on the grid points is of order $\frac{1}{2} - \epsilon$, $\epsilon>0$.

Subjects / Keywords

BSDE with oblique reflections; Discrete time approximation; Switching problems