Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs
Analysis of PDEs
2016-11-08 v3
Abstract
We study an expansion method for high-dimensional parabolic PDEs which constructs accurate approximate solutions by decomposition into solutions to lower-dimensional PDEs, and which is particularly effective if there are a low number of dominant principal components. The focus of the present article is the derivation of sharp error bounds for the constant coefficient case and a first and second order approximation. We give a precise characterisation when these bounds hold for (non-smooth) option pricing applications and provide numerical results demonstrating that the practically observed convergence speed is in agreement with the theoretical predictions.
Keywords
Cite
@article{arxiv.1505.04639,
title = {Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs},
author = {Christoph Reisinger and Rasmus Wissmann},
journal= {arXiv preprint arXiv:1505.04639},
year = {2016}
}