Numerical approximation of BSDEs using local polynomial drivers and branching processes
Provides a convergent numerical method for BSDEs that overcomes time horizon restrictions, benefiting researchers in stochastic control and mathematical finance.
Proposes a new numerical scheme for BSDEs using local polynomial drivers and branching processes, achieving convergence without time horizon limitations. Numerical simulations demonstrate performance.
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.