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Note on ``The smoothing effect of integration in $ \mathbb{R}^d$ and the ANOVA decomposition''


Authors: Michael Griebel, Frances Y. Kuo and Ian H. Sloan
Journal: Math. Comp. 86 (2017), 1847-1854
MSC (2010): Primary 41A63, 41A99; Secondary 65D30
DOI: https://doi.org/10.1090/mcom/3172
Published electronically: October 7, 2016
Original Article: Math. Comp. 82 (2013), 383-400.
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Abstract: This is a note on Math. Comp. 82 (2013), 383-400. We first report a mistake, in that the main result Theorem 3.1, though correct, does not as claimed apply to the Asian option pricing problem. This is because assumption (3.3) in the theorem is not satisfied by the Asian option pricing problem. In this note we present a strengthened theorem, which removes that assumption. The new theorem is immediately applicable to the Asian option pricing problem with the standard and Brownian bridge constructions. Thus the option pricing conclusions of our original paper stand.


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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
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/3172
Received by editor(s): June 23, 2015
Received by editor(s) in revised form: November 29, 2015
Published electronically: October 7, 2016
Article copyright: © Copyright 2016 American Mathematical Society