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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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Naumova, Mariya. Application of the discrete moment problem for numerical integration and solution of a special type of moment problems. Retrieved from https://doi.org/doi:10.7282/T3WS8W8G

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TitleApplication of the discrete moment problem for numerical integration and solution of a special type of moment problems
NameNaumova, Mariya (author); Ruszczynski, Andrzej (chair); Prekopa, Andras (internal member); Gurvich, Vladimir (internal member); Jeong, Myong K. (internal member); Baykal-Gursoy, Melike (outside member); Subasi, Munevver Mine (outside member); Rutgers University; Graduate School - New Brunswick
Date Created2015
Other Date2015-10 (degree)
SubjectOperations Research, Moment problems (Mathematics)
Extent1 online resource (v, 67 p. : ill.)
DescriptionWe 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.
NotePh.D.
NoteIncludes bibliographical references
Noteby Mariya Naumova
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T3WS8W8G
Languageeng
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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