Numerical approximation of BSDEs using local polynomial drivers and branching processes

Bruno Bouchard (1) , Xiaolu Tan (1) , Xavier Warin (2) , Yiyi Zou (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 EDF R&D - EDF R&D

We propose a new numerical scheme for Backward Stochastic Differential Equations based on branching processes. We approximate an arbitrary (Lipschitz) driver by local polynomials and then use a Picard iteration scheme. Each step of the Picard iteration can be solved by using a representation in terms of branching diffusion systems , thus avoiding the need for a fine time discretization. In contrast to the previous literature on the numerical resolution of BSDEs based on branching processes, we prove the convergence of our numerical scheme without limitation on the time horizon. Numerical simulations are provided to illustrate the performance of the algorithm.

Mots clés: Numerical methods; BSDE; Branching process

Domaines: Probabilités [math.PR]

Bruno Bouchard, Xiaolu Tan, Xavier Warin, Yiyi Zou. Numerical approximation of BSDEs using local polynomial drivers and branching processes. Monte Carlo Methods and Applications, 2017, 23 (4), pp.241-263. ⟨10.1515/mcma-2017-0116⟩. ⟨hal-01419981v2⟩