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Journal Articles Stochastic Processes and their Applications Year : 2008

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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Dates and versions

hal-00020697 , version 1 (14-03-2006)

Identifiers

  • HAL Id : hal-00020697 , version 1

Cite

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⟩
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