Fairbrother, Jamie (2016) Problemdriven scenario generation for stochastic programs. PhD thesis, UNSPECIFIED.

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Abstract
Stochastic programming concerns mathematical programming in the presence of uncertainty. In a stochastic program uncertain parameters are modeled as random vectors and one aims to minimize the expectation, or some risk measure, of a loss function. However, stochastic programs are computationally intractable when the underlying uncertain parameters are modeled by continuous random vectors. Scenario generation is the construction of a finite discrete random vector to use within a stochastic program. Scenario generation can consist of the discretization of a parametric probabilistic model, or the direct construction of a discrete distribution. There is typically a tradeoff here in the number of scenarios that are used: one must use enough to represent the uncertainty faithfully but not so many that the resultant problem is computationally intractable. Standard scenario generation methods are distributionbased, that is they do not take into account the underlying problem when constructing the discrete distribution. In this thesis we promote the idea of problembased scenario generation. By taking into account the structure of the underlying problem one may be able to represent uncertainty in a more parsimonious way. The first two papers of this thesis focus on scenario generation for problems which use a tailrisk measure, such as the conditional valueatrisk, focusing in particular on portfolio selection problems. In the final paper we present a constraint driven approach to scenario generation for simple recourse problems, a class of stochastic programs for minimizing the expected shortfall and surplus of some resources with respect to uncertain demands.
Item Type:  Thesis (PhD) 

Departments:  Faculty of Science and Technology > Mathematics and Statistics Lancaster University Management School > Management Science 
ID Code:  82869 
Deposited By:  ep_importer_pure 
Deposited On:  15 Nov 2016 09:40 
Refereed?:  No 
Published?:  Published 
Last Modified:  26 Feb 2020 00:12 
URI:  https://eprints.lancs.ac.uk/id/eprint/82869 
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