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Application of the discrete moment problem for numerical integration and solution of a special type of moment problems

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TitleInfo
Title
Application of the discrete moment problem for numerical integration and solution of a special type of moment problems
Name (type = personal)
NamePart (type = family)
Naumova
NamePart (type = given)
Mariya
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Mariya Naumova
Role
RoleTerm (authority = RULIB)
author
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Ruszczynski
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Andrzej
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Andrzej Ruszczynski
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Advisory Committee
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chair
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Prekopa
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Andras
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Andras Prekopa
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Advisory Committee
Role
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internal member
Name (type = personal)
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Gurvich
NamePart (type = given)
Vladimir
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Vladimir Gurvich
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Advisory Committee
Role
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internal member
Name (type = personal)
NamePart (type = family)
Jeong
NamePart (type = given)
Myong K.
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Myong K. Jeong
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Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Baykal-Gursoy
NamePart (type = given)
Melike
DisplayForm
Melike Baykal-Gursoy
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
outside member
Name (type = personal)
NamePart (type = family)
Subasi
NamePart (type = given)
Munevver Mine
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Munevver Mine Subasi
Affiliation
Advisory Committee
Role
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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
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theses
OriginInfo
DateCreated (encoding = w3cdtf); (qualifier = exact)
2015
DateOther (qualifier = exact); (type = degree)
2015-10
CopyrightDate (encoding = w3cdtf); (qualifier = exact)
2015
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
We present a brief survey of some of the basic results related to the classical continuous moment problems (CMP) and the recently developed discrete moment problems (DMP), clarifying their relationship. We also introduce a new numerical integration method, based on DMP and termed Discrete Moment Method (DMM), that can be used for univariate piecewise higher order convex functions. This means that the interval where the function is defined can be subdivided into non-overlapping subintervals such that in each interval all divided differences of given orders, do not change the sign. The new method uses piecewise polynomial lower and upper bounds on the function, created in connection with suitable dual feasible bases in the univariate discrete moment problem and the integral of the function is approximated by tight lower and upper bounds on them. Numerical illustrations are presented for the cases of the normal, exponential, gamma and Weibull probability density functions. We show how a similar approach can be applied for solving the problems of a special structure, namely the discrete conditional moment problems and present the corresponding numerical results. Finally, we present novel applications to valuations of financial instruments.
Subject (authority = RUETD)
Topic
Operations Research
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_6855
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
1 online resource (v, 67 p. : ill.)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Subject (authority = ETD-LCSH)
Topic
Moment problems (Mathematics)
Note (type = statement of responsibility)
by Mariya Naumova
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T3WS8W8G
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
Naumova
GivenName
Mariya
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2015-10-01 14:58:35
AssociatedEntity
Name
Mariya Naumova
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

RULTechMD (ID = TECHNICAL1)
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ETD
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windows xp
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