Discrete-time approximation for continuously and discretely reflected BSDEs

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:118

Article

Bouchard, Bruno^1,2  Chassagneux, Jean-Francois^2,3 

[1] Univ Paris 06, PMA, Paris, France

[2] CREST, Paris, France

[3] Univ Paris 07, PMA, Paris, France

关键词: Reflected BSDEs;    Discrete-time approximation schemes;    Regularity;   

DOI  :  10.1016/j.spa.2007.12.007

来源: Elsevier

【 摘 要 】

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 SIDE. 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 oil 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 epsilon C(b)(2) with the Lipschitz second derivative. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free