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Numerical approximation of general Lipschitz BSDEs with branching processes

Bouchard, Bruno; Tan, Xiaolu; Warin, Xavier (2019), Numerical approximation of general Lipschitz BSDEs with branching processes, ESAIM: Proceedings and Surveys, 65, p. 309-329. 10.1051/proc/201965309

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Type
Article accepté pour publication ou publié
Date
2019
Journal name
ESAIM: Proceedings and Surveys
Volume
65
Publisher
EDP Sciences
Pages
309-329
Publication identifier
10.1051/proc/201965309
Metadata
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Author(s)
Bouchard, Bruno

Tan, Xiaolu

Warin, Xavier
Abstract (EN)
We extend the branching process based numerical algorithm of Bouchard et al. [3], that is dedicated to semilinear PDEs (or BSDEs) with Lipschitz nonlinearity, to the case where the nonlinearity involves the gradient of the solution. As in [3], this requires a localization procedure that uses a priori estimates on the true solution, so as to ensure the well-posedness of the involved Picard iteration scheme, and the global convergence of the algorithm. When, the nonlinearity depends on the gradient, the later needs to be controlled as well. This is done by using a face-lifting procedure. Convergence of our algorithm is proved without any limitation on the time horizon. We also provide numerical simulations to illustrate the performance of the algorithm.
Subjects / Keywords
BSDE; Monte-Carlo methods; branching process

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