Volume 51, Number 6, November-December 2017
|Page(s)||2435 - 2463|
|Published online||18 December 2017|
Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs∗
1 Mathematical Institute and Oxford-Man Institute for Quantitative Finance, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG, United Kingdom.
2 Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG, United Kingdom.
Received: 7 May 2016
Revised: 31 October 2016
Accepted: 17 January 2017
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.
Mathematics Subject Classification: 35K15 / 65M06
Key words: High-dimensional PDEs / asymptotic expansions / anchored ANOVA / error bounds / financial derivative pricing
© EDP Sciences, SMAI 2017
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