Numerical approximation of BSDEs using local polynomial drivers and branching processes

Bouchard Bruno (), Tan Xiaolu (), Warin Xavier () and Zou Yiyi ()
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Bouchard Bruno: Université Paris-Dauphine, PSL Research University, CNRS, UMR [7534], Ceremade, 75016Paris, France
Tan Xiaolu: Université Paris-Dauphine, PSL Research University, CNRS, UMR [7534], Ceremade, 75016Paris, France
Warin Xavier: EDF/R&D, Laboratoire de Finance des Marchés de l’Energie, 92141ClamartCede, France
Zou Yiyi: Université Paris-Dauphine, PSL Research University, CNRS, UMR [7534], Ceremade, 75016Paris, France

Monte Carlo Methods and Applications, 2017, vol. 23, issue 4, 241-263

Abstract: We propose a new numerical scheme for Backward Stochastic Differential Equations (BSDEs) 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.

Keywords: BSDE; Monte Carlo methods; branching process (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1515/mcma-2017-0116

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