## Preliminary list of abstracts

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The smoothing effect of integration in $\mathbb{R}^d$ and the ANOVA decomposition
Keywords: smoothing; ANOVA decomposition
Sun, 16:35--17:00
• Kuo, Frances Y. (School of Mathematics and Statistics, University of New South Wales, Australia)
• Griebel, Michael (Institut für Numerische Simulation, University of Bonn, Germany)
• Sloan, Ian H. (School of Mathematics and Statistics, University of New South Wales, Australia)

We study the ANOVA decomposition of a $d$-variate function $f$ defined on the whole of $\mathbb{R}^d$, 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.