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The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth


Authors: Michael Griebel, Frances Y. Kuo and Ian H. Sloan
Journal: Math. Comp. 86 (2017), 1855-1876
MSC (2010): Primary 41A63, 41A99; Secondary 65D30
DOI: https://doi.org/10.1090/mcom/3171
Published electronically: October 7, 2016
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Abstract: The pricing problem for a continuous path-dependent option results in a path integral which can be recast into an infinite-dimensional integration problem. We study ANOVA decomposition of a function of infinitely many variables arising from the Brownian bridge formulation of the continuous option pricing problem. We show that all resulting ANOVA terms can be smooth in this infinite-dimensional case, despite the non-smoothness of the underlying payoff function. This result may explain why quasi-Monte Carlo methods or sparse grid quadrature techniques work for such option pricing problems.


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Michael Griebel
Affiliation: Institut für Numerische Simulation, Universität Bonn, Wegelerstrasse 6, 53115, Bonn, Germany – and – Fraunhofer Institute for Algorithms and Scientific Computing SCAI, Schloss Birlinghoven, 53754 Sankt Augustin, Germany
Email: griebel@ins.uni-bonn.de

Frances Y. Kuo
Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales 2052, Australia
Email: f.kuo@unsw.edu.au

Ian H. Sloan
Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales 2052, Australia
Email: i.sloan@unsw.edu.au

DOI: https://doi.org/10.1090/mcom/3171
Received by editor(s): May 14, 2014
Received by editor(s) in revised form: June 23, 2015, and November 29, 2015
Published electronically: October 7, 2016
Article copyright: © Copyright 2016 American Mathematical Society