Parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) have a wide range of applications. In particular, high-dimensional PDEs with gradient-dependent nonlinearities appear often in the state-of-the-art pricing and hedging of financial derivatives. In this article we prove that semilinear heat equations with gradient-dependent nonlinearities can be approximated under suitable assumptions with computational complexity that grows polynomially both in the dimension and the reciprocal of the accuracy.
@article{arxiv.1711.01080,
title = {Multi-level Picard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearities},
author = {Martin Hutzenthaler and Thomas Kruse},
journal= {arXiv preprint arXiv:1711.01080},
year = {2022}
}