A Numerical Scheme For High-dimensional Backward Stochastic Differential Equation Based On Modified Multi-level Picard Iteration

Abstract

In this paper, we propose a new kind of numerical scheme for high-dimensional backward stochastic differential equations based on modified multi-level Picard iteration. The proposed scheme is very similar to the original multi-level Picard iteration but it differs on underlying Monte-Carlo sample generation and enables an improvement in the sense of complexity. We prove the explicit error estimates for the case where the generator does not depend on control variate.

References in corpus (2)

• On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations
• Multi-level Picard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearities