# Discrete time approximation for continuously and discretely reflected BSDE's

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00020697
Contributor : Bruno Bouchard <>
Submitted on : Tuesday, March 14, 2006 - 4:11:40 PM
Last modification on : Thursday, December 10, 2020 - 11:08:24 AM
Long-term archiving on: : Wednesday, September 8, 2010 - 3:51:22 PM

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• HAL Id : hal-00020697, version 1

### Citation

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

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