Discrete-time Approximation of Multidimensional BSDEs with oblique reflections

Romuald Elie (1, 2) , Idris Kharroubi (2, 3) , Jean-François Chassagneux (4, 2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CREST - Centre de Recherche en Économie et Statistique
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
4 Département de Mathématiques (Evry)

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 $\frac{1}{2} - \epsilon$, $\epsilon>0$.

Mots clés: BSDE with oblique reflections; Discrete time approximation; Switching problems

Domaines: Probabilités [math.PR]

Romuald Elie, Idris Kharroubi, Jean-François Chassagneux. Discrete-time Approximation of Multidimensional BSDEs with oblique reflections. The Annals of Applied Probability, 2012, 22 (3), pp 971 - 1007. ⟨hal-00475628⟩