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Time-consistent approximations of risk-averse multistage stochastic optimization problems
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Asamov, Tsvetan. Time-consistent approximations of risk-averse multistage stochastic optimization problems. Retrieved from https://doi.org/doi:10.7282/T3M906P7

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TitleTime-consistent approximations of risk-averse multistage stochastic optimization problems
NameAsamov, Tsvetan (author); Ruszczynski, Andrzej (chair); BEN-ISRAEL, ADI (internal member); Elsayed, Elsayed A. (internal member); Roberts, Fred (internal member); Dentcheva, Darinka (outside member); Rutgers University; Graduate School - New Brunswick
Date Created2013
Other Date2013-10 (degree)
SubjectOperations Research, Stochastic processes, Operations research, Time management
Extentx, 91 p. : ill.
DescriptionIn this work we study the concept of time consistency as it relates to multistage risk-averse stochastic optimization problems on finite scenario trees. We use dynamic time-consistent formulations to approximate problems having a single global coherent risk measure applied to the aggregated costs over all time periods. The duality of coherent risk measures is employed to create a time-consistent cutting plane algorithm for the construction of non-parametric time-consistent approximations where every one- step conditional risk measure is specified only by its dual representation. Moreover, we show that the method can be extended to generate parametric approximations involving compositions of risk measures from a specified family. Additionally, we also consider the case when the objective function is the mean-upper semideviation measure of risk and develop methods for the construction of universal time-consistent upper bounding functions. We prove that such functions provide time-consistent upper bounds to the global risk measure for an arbitrary feasible policy. Finally, the quality of the approximations generated by the proposed methods is analyzed in multiple computational experiments involving two-stage scenario trees with both artificial data, as well as stock return data for the components of the Dow Jones Industrial Average stock market index. Our numerical results indicate that the dynamic time-consistent formulations closely approximate the original problem for a wide range of risk aversion parameters.
NotePh.D.
NoteIncludes bibliographical references
NoteIncludes vita
Noteby Tsvetan Asamov
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T3M906P7
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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