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Strong Approximations of BSDEs in a domain

Menozzi, Stéphane; Bouchard, Bruno (2009), Strong Approximations of BSDEs in a domain, Bernoulli, 15, 4, p. 1117-1147. http://dx.doi.org/10.3150/08-BEJ181

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00177481/en/
Date
2009
Journal name
Bernoulli
Volume
15
Number
4
Publisher
Bernoulli Society
Pages
1117-1147
Publication identifier
http://dx.doi.org/10.3150/08-BEJ181
Metadata
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Author(s)
Menozzi, Stéphane
Bouchard, Bruno
Abstract (EN)
We study the strong approximation of a Backward SDE with finite stopping time horizon, namely the first exit time of a forward SDE from a cylindrical domain. We use the Euler scheme approach of Bouchard and Touzi, Zhang 04}. When the domain is piecewise smooth and under a non-characteristic boundary condition, we show that the associated strong error is at most of order $h^{\frac14-\eps}$ where $h$ denotes the time step and $\eps$ is any positive parameter. This rate corresponds to the strong exit time approximation. It is improved to $h^{\frac12-\eps}$ when the exit time can be exactly simulated or for a weaker form of the approximation error. Importantly, these results are obtained without uniform ellipticity condition.
Subjects / Keywords
Approximation a temps discret; EDS progressives retrogrades; Probleme de Cauchy semilineaire

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