Discrete-time approximation for continuously and discretely reflected BSDEs

We study the discrete-time approximation of the solution (Y,Z,K) of a reflected BSDE. As in Ma and Zhang [J. Ma, J. Zhang, Representations and regularities for solutions to BSDEs with reflections, Stochastic Processes and their Applications 115 (2005) 539-569], 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 [J. Ma, J. Zhang, Representations and regularities for solutions to BSDEs with reflections, Stochastic Processes and their Applications 115 (2005) 539-569] 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 with the Lipschitz second derivative.