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

## TL;DR

This paper introduces a novel numerical scheme for high-dimensional backward stochastic differential equations using a modified multi-level Picard iteration, improving computational complexity and providing explicit error estimates.

## Contribution

It presents a new numerical scheme based on a modified multi-level Picard iteration that enhances efficiency for high-dimensional BSDEs and includes explicit error bounds.

## Key findings

- Improved complexity over traditional methods
- Explicit error estimates for generator-independent cases
- Effective handling of high-dimensional problems

## 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.