2017
DOI: 10.1051/m2an/2017003
|View full text |Cite
|
Sign up to set email alerts
|

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

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 applic… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

0
8
0

Year Published

2018
2018
2021
2021

Publication Types

Select...
3

Relationship

0
3

Authors

Journals

citations
Cited by 3 publications
(8 citation statements)
references
References 34 publications
0
8
0
Order By: Relevance
“…A rigorous error analysis of the PCA-based approximation relevant to European basket options has been given by Reisinger & Wissmann [4]. In particular, under mild assumptions, these authors showed that w´r w " O`λ 2 2˘i n the maximum norm.…”
Section: Pca-based Approximation For European Basket Optionmentioning
confidence: 99%
See 3 more Smart Citations
“…A rigorous error analysis of the PCA-based approximation relevant to European basket options has been given by Reisinger & Wissmann [4]. In particular, under mild assumptions, these authors showed that w´r w " O`λ 2 2˘i n the maximum norm.…”
Section: Pca-based Approximation For European Basket Optionmentioning
confidence: 99%
“…Reisinger & Wissmann [4] have given a rigorous analysis of the error in the PCA-based approximation relevant to European basket options. Under a mild assumption on the payoff function φ, they proved that w − w = O λ 2 2 in the maximum norm.…”
Section: Writementioning
confidence: 99%
See 2 more Smart Citations
“…• compared to Reisinger and Wissmann (2015) which provides error bounds for the constant coefficient setting, we deal with the case of non-linear SDEs and variable-coefficient PDEs, which requires a generalised definition of the expansion;…”
Section: Introductionmentioning
confidence: 99%