Discrete time approximation for continuously and discretely reflected BSDE's

Bruno Bouchard (1, 2) , Jean-François Chassagneux (1, 2)

1 LFA - Laboratoire de Finance Assurance
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We study the discrete time approximation of the solution $(Y,Z,K)$ of a reflected BSDE. As in Ma and Zhang (2005), we consider a markovian setting with a reflecting barrier of the form $h(X)$ where $X$ solves a forward SDE. We first focus on the discretely reflected case. Based on a representation for the $Z$ component in terms of the next reflection time, we retrieve the convergence result of Ma and Zhang (2005) without their uniform ellipticity condition on $X$. These results are then extended to the case where the reflection operates continuously. We also improve the bound on the convergence rate when $h \in C^2_b$ with Lipschitz second derivative.

Mots clés: Reflected BSDEs; discrete-time approximation schemes; regularity

Domaines: Probabilités [math.PR]

Bruno Bouchard, Jean-François Chassagneux. Discrete time approximation for continuously and discretely reflected BSDE's. Stochastic Processes and their Applications, 2008, 118, pp.2269-2293. ⟨hal-00020697⟩