2012/10/04 by Jean-Francois Chassagneux, Romuald Elie, Idris Kharroubi · 1 citation
Mathematics · #math.PR
paper · pdf · doi:10.1214/11-aap771
published as Annals of Applied Probability 2012, Vol. 22, No. 3, 971-1007 · 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)
arxiv created 2012/10/04 · arxiv updated 2012/10/05
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 1/2-ε, ε>0.