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dc.contributor.author
Reich, N.
dc.contributor.author
Schwab, Christoph
dc.contributor.author
Winter, C.
dc.date.accessioned
2017-06-08T20:30:12Z
dc.date.available
2017-06-08T20:30:12Z
dc.date.issued
2008
dc.identifier.uri
http://hdl.handle.net/20.500.11850/12077
dc.description.abstract
For d-dimensional exponential L´evy models, variational formulations of the Kolmogorov equations arising in asset pricing are derived. Well-posedness of these equations is verified. Particular attention is paid to pure jump, d-variate L´evy processes built from parametric, copula dependence models in their jump structure. The domains of the associated Dirichlet forms are shown to be certain anisotropic Sobolev spaces. Representations of the Dirichlet forms are given which remain bounded for piecewise polynomial, continuous functions of finite element type. We prove that the variational problem can be localized to a bounded domain with explicit localization error bounds. Furthermore, we collect several analytical tools for further numerical analysis.
dc.language.iso
en
dc.publisher
Seminar für Angewandte Mathematik, ETH
dc.subject
L´evy-copulas
dc.subject
L´evy processes
dc.subject
integrodifferential equations
dc.subject
pseudo differential operators
dc.subject
Dirichlet forms
dc.subject
option pricing
dc.title
On Kolmogorov equations for anisotropic multivariate Lévy processes
dc.type
Report
ethz.journal.title
Research reports
ethz.journal.issue
3
ethz.journal.abbreviated
Res. rep.- Natl. Geogr. Soc.
ethz.size
30 p.
ethz.identifier.nebis
000021043
ethz.publication.place
Zürich
ethz.publication.status
published
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03435 - Schwab, Christoph / Schwab, Christoph
ethz.leitzahl
03217 - Künsch, Hans Rudolf
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03435 - Schwab, Christoph / Schwab, Christoph
ethz.leitzahl.certified
03217 - Künsch, Hans Rudolf
ethz.identifier.url
ftp://ftp.sam.math.ethz.ch/pub/sam-reports/reports/reports2008/2008-03.pdf
ethz.date.deposited
2017-06-08T20:30:33Z
ethz.source
ECIT
ethz.identifier.importid
imp59364c107fe8645631
ethz.ecitpid
pub:23347
ethz.eth
yes
ethz.availability
Metadata only
ethz.rosetta.installDate
2017-07-19T11:17:44Z
ethz.rosetta.lastUpdated
2022-03-28T08:04:30Z
ethz.rosetta.exportRequired
true
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true
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