The Annals of Applied Probability

Discrete-time approximation of multidimensional BSDEs with oblique reflections

Jean-Francois Chassagneux, Romuald Elie, and Idris Kharroubi

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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.

Article information

Ann. Appl. Probab., Volume 22, Number 3 (2012), 971-1007.

First available in Project Euclid: 18 May 2012

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Zentralblatt MATH identifier

Primary: 93E20: Optimal stochastic control 65C99: None of the above, but in this section
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)

BSDE with oblique reflections discrete time approximation switching problems


Chassagneux, Jean-Francois; Elie, Romuald; Kharroubi, Idris. Discrete-time approximation of multidimensional BSDEs with oblique reflections. Ann. Appl. Probab. 22 (2012), no. 3, 971--1007. doi:10.1214/11-AAP771.

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