The smoothing effect of integration in Rd and the ANOVA decomposition

نویسندگان

  • Michael Griebel
  • Frances Y. Kuo
  • Ian H. Sloan
چکیده

This paper studies the ANOVA decomposition of a d-variate function f defined on the whole of Rd, 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. 2010 Mathematics Subject Classification: Primary 41A63, 41A99. Secondary 65D30.

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عنوان ژورنال:
  • Math. Comput.

دوره 82  شماره 

صفحات  -

تاریخ انتشار 2013