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Problem-driven scenario generation for stochastic programs

Research output: ThesisDoctoral Thesis

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Problem-driven scenario generation for stochastic programs. / Fairbrother, Jamie.

Lancaster University, 2016. 215 p.

Research output: ThesisDoctoral Thesis

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@phdthesis{f77bfa1a8ef94e83ad749cadebcb9d5b,
title = "Problem-driven scenario generation for stochastic programs",
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 trade-off 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 distribution-based, that is they do not take into account the underlying problem when constructing the discrete distribution.In this thesis we promote the idea of problem-based 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 tail-risk measure, such as the conditional value-at-risk, 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.",
author = "Jamie Fairbrother",
year = "2016",
language = "English",
publisher = "Lancaster University",
school = "Lancaster University",

}

RIS

TY - THES

T1 - Problem-driven scenario generation for stochastic programs

AU - Fairbrother, Jamie

PY - 2016

Y1 - 2016

N2 - 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 trade-off 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 distribution-based, that is they do not take into account the underlying problem when constructing the discrete distribution.In this thesis we promote the idea of problem-based 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 tail-risk measure, such as the conditional value-at-risk, 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.

AB - 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 trade-off 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 distribution-based, that is they do not take into account the underlying problem when constructing the discrete distribution.In this thesis we promote the idea of problem-based 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 tail-risk measure, such as the conditional value-at-risk, 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.

M3 - Doctoral Thesis

PB - Lancaster University

ER -