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Degenerate partial differential equations and applications to probability theory and foundations of mathematical finance

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Title
Degenerate partial differential equations and applications to probability theory and foundations of mathematical finance
Name (type = personal)
NamePart (type = family)
Pop
NamePart (type = given)
Camelia Alexandra
NamePart (type = date)
1983-
DisplayForm
Camelia Pop
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Feehan
NamePart (type = given)
Paul M. N.
DisplayForm
Paul M. N. Feehan
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
chair
Name (type = personal)
NamePart (type = family)
Ocone
NamePart (type = given)
Daniel
DisplayForm
Daniel Ocone
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Han
NamePart (type = given)
Zheng-Chao
DisplayForm
Zheng-Chao Han
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Gundy
NamePart (type = given)
Richard
DisplayForm
Richard Gundy
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
DASKALOPOULOS
NamePart (type = given)
PANAGIOTA
DisplayForm
PANAGIOTA DASKALOPOULOS
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
outside member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (qualifier = exact)
2012
DateOther (qualifier = exact); (type = degree)
2012-05
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
In the first part of our thesis, we prove existence, uniqueness and regularity of solutions for a certain class of degenerate parabolic partial differential equations on the half space which are a generalization of the Heston operator. We use these results to show that the martingale problem associated with the differential operator is well-posed and we build generalized Heston-like processes which match the one-dimensional probability distributions of a certain class of It^o processes. The second part of our thesis is concerned with the study of regularity of solutions to the variational equation associated to the elliptic Heston operator. With the aid of weighted Sobolev spaces, we prove supremum bounds, a Harnack inequality, and H"older continuity near the boundary for solutions to elliptic variational equations defined by the Heston partial differential operator. Finally, we establish stochastic representations of solutions to elliptic and parabolic boundary value problems and obstacle problems associated to the Heston generator. In mathematical finance, solutions to parabolic obstacle problems correspond to value functions for American-style options.
Subject (authority = RUETD)
Topic
Mathematics
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_3920
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
viii, 228 p. : ill.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Camelia Alexandra Pop
Subject (authority = ETD-LCSH)
Topic
Differential equations, Partial
Subject (authority = ETD-LCSH)
Topic
Degenerate differential equations
Subject (authority = ETD-LCSH)
Topic
Finance--Mathematical models
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000065245
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/T30K27HB
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Pop
GivenName
Camelia
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2012-04-12 10:03:25
AssociatedEntity
Name
Camelia Pop
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
Type
License
Name
Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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Technical

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1734144
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application/pdf
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application/x-tar
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1740800
Checksum (METHOD = SHA1)
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