Geodesic
Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs
Reisinger, Christoph1  ; Wissmann, Rasmus2
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.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 6, pp. 2435-2463

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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.

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Accepté le :
DOI : 10.1051/m2an/2017003
Classification : 35K15, 65M06
Keywords: High-dimensional PDEs, asymptotic expansions, anchored ANOVA, error bounds, financial derivative pricing

Reisinger, Christoph 1 ; Wissmann, Rasmus 2

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. 
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     author = {Reisinger, Christoph and Wissmann, Rasmus},
     title = {Error analysis of truncated expansion solutions to high-dimensional parabolic {PDEs}},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {2435--2463},
     publisher = {EDP-Sciences},
     volume = {51},
     number = {6},
     year = {2017},
     doi = {10.1051/m2an/2017003},
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     zbl = {1382.65280},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017003/}
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Reisinger, Christoph; Wissmann, Rasmus. Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 6, pp. 2435-2463. doi: 10.1051/m2an/2017003

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