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DOI: 10.4230/DagSemProc.09391.3
URN: urn:nbn:de:0030-drops-22987
URL: https://drops.dagstuhl.de/opus/volltexte/2009/2298/
Hickernell, Fred J. ; Müller-Gronbach, Thomas ; Niu, Ben ; Ritter, Klaus
Evaluating Expectations of Functionals of Brownian Motions: a Multilevel Idea
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Abstract
Prices of path dependent options may be modeled as expectations of functions of an infinite sequence of real variables. This talk presents recent work on bounding the error of such expectations using quasi-Monte Carlo algorithms. The expectation is approximated by an average of $n$ samples, and the functional of an infinite number of variables is approximated by a function of only $d$ variables. A multilevel algorithm employing a sum of sample averages, each with different truncated dimensions, $d_l$, and different sample sizes, $n_l$, yields faster convergence than a single level algorithm. This talk presents results in the worst-case error setting.
BibTeX - Entry
@InProceedings{hickernell_et_al:DagSemProc.09391.3,
author = {Hickernell, Fred J. and M\"{u}ller-Gronbach, Thomas and Niu, Ben and Ritter, Klaus},
title = {{Evaluating Expectations of Functionals of Brownian Motions: a Multilevel Idea}},
booktitle = {Algorithms and Complexity for Continuous Problems},
pages = {1--19},
series = {Dagstuhl Seminar Proceedings (DagSemProc)},
ISSN = {1862-4405},
year = {2009},
volume = {9391},
editor = {Thomas M\"{u}ller-Gronbach and Leszek Plaskota and Joseph. F. Traub},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2009/2298},
URN = {urn:nbn:de:0030-drops-22987},
doi = {10.4230/DagSemProc.09391.3},
annote = {Keywords: Brownian motions, multilevel, option pricing, worst-case error}
}
| Keywords: | Brownian motions, multilevel, option pricing, worst-case error | |
| Seminar: | 09391 - Algorithms and Complexity for Continuous Problems | |
| Issue date: | 2009 | |
| Date of publication: | 02.12.2009 |
