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Article Dans Une Revue ESAIM: Proceedings and Surveys Année : 2019

Numerical approximation of general Lipschitz BSDEs with branching processes

Xavier Warin
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Résumé

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.
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Dates et versions

hal-01626034 , version 1 (30-10-2017)

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Bruno Bouchard, Xiaolu Tan, Xavier Warin. Numerical approximation of general Lipschitz BSDEs with branching processes. ESAIM: Proceedings and Surveys, 2019, 65, pp.309-329. ⟨hal-01626034⟩
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