Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs

Author: 

Reisinger, C
Wissmann, R

Publication Date: 

1 December 2017

Journal: 

ESAIM: Mathematical Modelling and Numerical Analysis

Last Updated: 

2020-01-21T14:50:42.937+00:00

Issue: 

6

Volume: 

51

DOI: 

10.1051/m2an/2017003

page: 

2435-2463

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 (nonsmooth) option pricing applications and provide numerical results demonstrating that the practically observed convergence speed is in agreement with the theoretical predictions.

Symplectic id: 

673892

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article