Deterministic approximations in stochastic programming with applications to a class of portfolio allocation problems

dc.contributor.advisorMorton, David P.en
dc.creatorDokov, Steftcho Pentcheven
dc.date.accessioned2011-03-09T16:27:24Zen
dc.date.available2011-03-09T16:27:24Zen
dc.date.issued2001-08en
dc.descriptiontexten
dc.description.abstractOptimal decision making under uncertainty involves modeling stochastic systems and developing solution methods for such models. The need to incorporate randomness in many practical decision-making problems is prompted by the uncertainties associated with today’s fast-paced technological environment. The complexity of the resulting models often exceeds the capabilities of commercially available optimization software, and special purpose solution techniques are required. Three main categories of solution approaches exist for attacking a particular stochastic programming instance. These are: large-scale mathematical programming algorithms, Monte-Carlo sampling-based techniques, and deterministically valid bound-based approximations. This research contributes to the last category. First, second-order lower and upper bounds are developed on the expectation of a convex function of a random vector. Here, a “second-order bound” means that only the first and second moments of the underlying random parameters are needed to compute the bound. The vector’s random components are assumed to be independent and to have bounded support contained in a hyper-rectangle. Applications to stochastic programming test problems and analysis of numerical performance are also presented. Second, assuming additional relevant moment information is available, higher-order upper bounds are developed. In this case the underlying random vector can have support contained in either a hyper-rectangle or a multidimensional simplex, and the random parameters can be either dependent or independent. The higher-order upper bounds form a decreasing sequence converging to the true expectation, and yielding convergence of the optimal decisions. Finally, applications of the higher-order upper bounds to a class of portfolio optimization problems are presented. Mean-variance and mean-varianceskewness efficient portfolio frontiers are considered in the context of a specific portfolio allocation model as well as in general and connected with applications of the higher-order upper bounds in utility theory
dc.description.departmentMechanical Engineeringen
dc.format.mediumelectronicen
dc.identifier.urihttp://hdl.handle.net/2152/10405en
dc.rightsCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.en
dc.rights.restrictionRestricteden
dc.subjectStochastic programmingen
dc.subjectStochastic approximationen
dc.subjectMathematical optimizationen
dc.titleDeterministic approximations in stochastic programming with applications to a class of portfolio allocation problemsen
thesis.degree.departmentMechanical Engineeringen
thesis.degree.disciplineManufacturing and Decision Systems Engineeringen
thesis.degree.grantorThe University of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen

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