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
TypeArticle accepté pour publication ou publié
Journal nameESAIM: Proceedings and Surveys
MetadataShow full item record
Abstract (EN)We extend the branching process based numerical algorithm of Bouchard et al. , 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 , 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 / KeywordsBSDE; Monte-Carlo methods; branching process
Showing items related by title and author.
Henry-Labordère, Pierre; Oudjane, Nadia; Tan, Xiaolu; Touzi, Nizar; Warin, Xavier (2017) Document de travail / Working paper
Bouchard, Bruno; Possamaï, Dylan; Tan, Xiaolu; Zhou, Chao (2017) Article accepté pour publication ou publié
Bouchard, Bruno; Possamaï, Dylan; Tan, Xiaolu; Zhou, Chao (2018) Article accepté pour publication ou publié