Numerical approximation of general Lipschitz BSDEs with branching processes

Bouchard, Bruno; Tan, Xiaolu; Warin, Xavier

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

Publisher

EDP Sciences

Pages

309-329

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