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Discrete time approximation for continuously and discretely reflected BSDE's

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Date
2008
Dewey
Probabilités et mathématiques appliquées
Sujet
Discrete-time approximation schemes; Numerical Probability
Journal issue
Stochastic Processes and their Applications
Volume
118
Number
12
Publication date
12-2008
Article pages
2269-2293
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.spa.2007.12.007
URI
https://basepub.dauphine.fr/handle/123456789/1928
Collections
  • CEREMADE : Publications
Metadata
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Author
Chassagneux, Jean-François
Bouchard, Bruno
Type
Article accepté pour publication ou publié
Abstract (EN)
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 View the MathML source with the Lipschitz second derivative.

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