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.
Accepté le :
DOI : 10.1051/m2an/2017003
Mots clés : High-dimensional PDEs, asymptotic expansions, anchored ANOVA, error bounds, financial derivative pricing
@article{M2AN_2017__51_6_2435_0, 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}, mrnumber = {3745177}, zbl = {1382.65280}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2017003/} }
TY - JOUR AU - Reisinger, Christoph AU - Wissmann, Rasmus TI - Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 2435 EP - 2463 VL - 51 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2017003/ DO - 10.1051/m2an/2017003 LA - en ID - M2AN_2017__51_6_2435_0 ER -
%0 Journal Article %A Reisinger, Christoph %A Wissmann, Rasmus %T Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 2435-2463 %V 51 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2017003/ %R 10.1051/m2an/2017003 %G en %F M2AN_2017__51_6_2435_0
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. http://www.numdam.org/articles/10.1051/m2an/2017003/
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