The smoothing effect of integration in ℝd and the ANOVA decomposition
The smoothing effect of integration in ℝd and the ANOVA decomposition
View/Date of Publication
12.2010Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
Show full item record
Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11964
Abstract
This paper studies the ANOVA decomposition of a d-variate function f defined on the whole of ℝd, where f is the maximum of a smooth function and zero (or f could be the absolute value of a smooth function). Our study is motivated by option pricing problems. We show that under suitable conditions all terms of the ANOVA decomposition, except the one of highest order, can have unlimited smoothness. In particular, this is the case for arithmetic Asian options with both the standard and Brownian bridge constructions of the Brownian motion.
Subjects
ANOVA decomposition, smoothing, option pricing
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1090/S0025-5718-2012-02578-6Part of Series
INS Preprints ; 1007Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H.: The smoothing effect of integration in ℝd and the ANOVA decomposition. In: INS Preprints, 1007.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11964
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11964
@unpublished{handle:20.500.11811/11964,
author = {{Michael Griebel} and {Frances Y. Kuo} and {Ian H. Sloan}},
title = {The smoothing effect of integration in ℝd and the ANOVA decomposition},
publisher = {Institut für Numerische Simulation (INS)},
year = 2010,
month = dec,
INS Preprints},
volume = 1007,
note = {This paper studies the ANOVA decomposition of a d-variate function f defined on the whole of ℝd, where f is the maximum of a smooth function and zero (or f could be the absolute value of a smooth function). Our study is motivated by option pricing problems. We show that under suitable conditions all terms of the ANOVA decomposition, except the one of highest order, can have unlimited smoothness. In particular, this is the case for arithmetic Asian options with both the standard and Brownian bridge constructions of the Brownian motion.},
url = {https://hdl.handle.net/20.500.11811/11964}
}
author = {{Michael Griebel} and {Frances Y. Kuo} and {Ian H. Sloan}},
title = {The smoothing effect of integration in ℝd and the ANOVA decomposition},
publisher = {Institut für Numerische Simulation (INS)},
year = 2010,
month = dec,
INS Preprints},
volume = 1007,
note = {This paper studies the ANOVA decomposition of a d-variate function f defined on the whole of ℝd, where f is the maximum of a smooth function and zero (or f could be the absolute value of a smooth function). Our study is motivated by option pricing problems. We show that under suitable conditions all terms of the ANOVA decomposition, except the one of highest order, can have unlimited smoothness. In particular, this is the case for arithmetic Asian options with both the standard and Brownian bridge constructions of the Brownian motion.},
url = {https://hdl.handle.net/20.500.11811/11964}
}
The following license files are associated with this item:
