Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs
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...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Published: |
EDP Sciences
2017
|
| _version_ | 1826259725675659264 |
|---|---|
| author | Reisinger, C Wissmann, R |
| author_facet | Reisinger, C Wissmann, R |
| author_sort | Reisinger, C |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T18:54:20Z |
| format | Journal article |
| id | oxford-uuid:1149be95-1268-4e55-af73-919644558622 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:54:20Z |
| publishDate | 2017 |
| publisher | EDP Sciences |
| record_format | dspace |
| spelling | oxford-uuid:1149be95-1268-4e55-af73-9196445586222022-03-26T10:01:34ZError analysis of truncated expansion solutions to high-dimensional parabolic PDEsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1149be95-1268-4e55-af73-919644558622Symplectic Elements at OxfordEDP Sciences2017Reisinger, CWissmann, RWe 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. |
| spellingShingle | Reisinger, C Wissmann, R Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs |
| title | Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs |
| title_full | Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs |
| title_fullStr | Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs |
| title_full_unstemmed | Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs |
| title_short | Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs |
| title_sort | error analysis of truncated expansion solutions to high dimensional parabolic pdes |
| work_keys_str_mv | AT reisingerc erroranalysisoftruncatedexpansionsolutionstohighdimensionalparabolicpdes AT wissmannr erroranalysisoftruncatedexpansionsolutionstohighdimensionalparabolicpdes |