Numerical approximation of BSDEs using local polynomial drivers and branching processes

2016/12/20 by Bruno Bouchard, Xiaolu Tan, Bouchard, Bruno +5
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60H35 #60J60 #FOS: Mathematics #Mathematical Biology Tumor Growth #Numerical Analysis (math.NA) #Primary 65C05 #Risk and Portfolio Optimization #Secondary 60J85 #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1612.06790

openalex publication_date 2016/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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.

Citations

• Adaptive sparse grids for time dependent Hamilton-Jacobi-Bellman equations in stochastic control

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