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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth
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by Michael Griebel, Frances Y. Kuo and Ian H. Sloan PDF
Math. Comp. 86 (2017), 1855-1876 Request permission

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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Additional Information
  • 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
  • MR Author ID: 270664
  • 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
  • MR Author ID: 703418
  • 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
  • MR Author ID: 163675
  • ORCID: 0000-0003-3769-0538
  • Email: i.sloan@unsw.edu.au
  • 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
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 1855-1876
  • MSC (2010): Primary 41A63, 41A99; Secondary 65D30
  • DOI: https://doi.org/10.1090/mcom/3171
  • MathSciNet review: 3626540