Discrete-time approximation for continuously and discretely reflected BSDEs

We study the discrete-time approximation of the solution (Y,Z,K)(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)h(X) where XX solves a forward SDE. We first focus on the discretely reflected case. Based on a representation for the ZZ 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 XX. These results are then extended to the case where the reflection operates continuously. We also improve the bound on the convergence rate when h∈Cb2 with the Lipschitz second derivative.