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June 2012 Discrete-time approximation of multidimensional BSDEs with oblique reflections
Jean-Francois Chassagneux, Romuald Elie, Idris Kharroubi
Ann. Appl. Probab. 22(3): 971-1007 (June 2012). DOI: 10.1214/11-AAP771

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 Hamadène and Zhang [Stochastic Process. Appl. 120 (2010) 403–426]. In comparison to the penalizing approach followed by Hamadène 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 Z, the error on the grid points is of order ½ − ε, ε > 0.

Citation

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Jean-Francois Chassagneux. Romuald Elie. Idris Kharroubi. "Discrete-time approximation of multidimensional BSDEs with oblique reflections." Ann. Appl. Probab. 22 (3) 971 - 1007, June 2012. https://doi.org/10.1214/11-AAP771

Information

Published: June 2012
First available in Project Euclid: 18 May 2012

zbMATH: 1243.93128
MathSciNet: MR2977983
Digital Object Identifier: 10.1214/11-AAP771

Subjects:
Primary: 65C99, 93E20
Secondary: 60H30

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.22 • No. 3 • June 2012
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