The branching methods developed are effective methods to solve some semi linear PDEs and are shown numerically to be able to solve some full non linear PDEs. These methods are however restricted to some small coefficients in the PDE and small maturities. This article shows numerically that these methods can be adapted to solve the problems with longer maturities in the semi-linear case by using a new derivation scheme and some nested method. As for the case of full non linear PDEs, we introduce new schemes and we show numerically that they provide an effective alternative to the schemes previously developed.
Branching diffusion representation of semilinear PDEs and Monte Carlo approximation
Société Générale, Global Market Quantitative Research（法国兴业银行，全球市场量化研究）；EDF R&D & FiME, Laboratoire de Finance des Marchés de l’Energie（法国电力集团研发部及能源金融市场金融研究所，能源市场金融实验室）；CEREMADE, University of Paris-Dauphine, PSL Research University（巴黎第九大学数学与决策研究中心，PSL研究大学）；Ecole Polytechnique Paris, Centre de Mathématiques Appliquées（巴黎综合理工学院，应用数学中心）
A numerical algorithm for a class of BSDEs via branching process
Société Générale, Global Market Quantitative Research（法国兴业银行全球市场量化研究部）；CEREMADE, University of Paris-Dauphine（巴黎第九大学 CEREMADE 中心）；Ecole Polytechnique Paris, Centre de Mathématiques Appliquées（巴黎综合理工学院应用数学中心）
Hybrid PDE solver for data-driven problems and modern branching
CMAP - Centre de Mathématiques Appliquées, Ecole Polytechnique（应用数学中心，巴黎综合理工学院）；University of Edinburgh（爱丁堡大学）；Centro de Matemática e Aplicaç o ~ \tilde{\text{o}} es (CMA), FCT, UNL（数学与应用中心，法蒂玛科技大学，新里斯本大学）；Maxwell Institute Graduate School in Analysis and its Applications (MIGSAA), University of Edinburgh（麦克斯韦分析及其应用研究生学院，爱丁堡大学）
