Preliminary list of abstracts

Note: We are using the fantastic MathJax JavaScript library to typeset the mathematics on this web page. You can right-click on a formula to zoom in or to select the rendering engine you like (all under 'Settings'). Under Firefox the default renderer turns out to be MathML (which is quick), but you might prefer the HTML-CSS renderer for more faithful LaTeX rendering. If you encounter any problems with this setup: then please email us!

Click here to go back to the list of abstracts.

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.