A Numerical Scheme For High-dimensional Backward Stochastic Differential Equation Based On Modified Multi-level Picard Iteration
For researchers working on numerical methods for high-dimensional BSDEs, this work offers a complexity improvement over existing multi-level Picard iteration, though it is an incremental modification.
This paper proposes a modified multi-level Picard iteration scheme for high-dimensional backward stochastic differential equations, achieving improved computational complexity while providing explicit error estimates for the case where the generator does not depend on control variate.
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.