<div class="csl-bib-body">
<div class="csl-entry">Gudat, E. (2015). <i>Convergence analysis of the Longstaff-Schwartz algorithm</i> [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2015.27818</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2015.27818
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/3153
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dc.description.abstract
We analyse convergence properties of the Longstaff-Schwartz algorithm, a routine used in pricing American options. After a description and a numerical example of the algorithm, we will present an introduction to statistical learning theory and give a rigorous proof of Pollard's inequality. Having established the Vapnik-Chervonenkis dimension, we pass on to prove an inequality about the error that occurs within one step of the LS-Algorithm. We use all this to establish convergence theorems, even in settings where the approximation spaces are not convex, closed or linear, as long as they are uniformly bounded and have a finite Vapnik-Chervonenkis dimension. The rest of the thesis deals with applications of the convergence theorems. We are going to use polynomial approximations architectures and artificial neural networks.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
Option pricing
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dc.subject
American option
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dc.subject
Longstaff-Schwartz algorithm
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dc.subject
statistical learning
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dc.title
Convergence analysis of the Longstaff-Schwartz algorithm
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dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2015.27818
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Emanuel Gudat
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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tuw.publication.orgunit
E105 - Institut für Stochastik und Wirtschaftsmathematik