- paper_1_arxiv
Submitted manuscript, 526 KB, PDF document

- http://arxiv.org/abs/1511.03074
Final published version

Research output: Contribution to journal › Journal article

E-pub ahead of print

**Problem-driven scenario generation : an analytical approach for stochastic programs with tail risk measure.** / Fairbrother, Jamie; Turner, Amanda; Wallace, Stein W.

Research output: Contribution to journal › Journal article

Fairbrother, J, Turner, A & Wallace, SW 2015, 'Problem-driven scenario generation: an analytical approach for stochastic programs with tail risk measure', *arxiv.org*. <http://arxiv.org/abs/1511.03074 >

Fairbrother, J., Turner, A., & Wallace, S. W. (2015). Problem-driven scenario generation: an analytical approach for stochastic programs with tail risk measure. *arxiv.org*. http://arxiv.org/abs/1511.03074

Fairbrother J, Turner A, Wallace SW. Problem-driven scenario generation: an analytical approach for stochastic programs with tail risk measure. arxiv.org. 2015 Nov.

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title = "Problem-driven scenario generation: an analytical approach for stochastic programs with tail risk measure",

abstract = "Scenario generation is the construction of a discrete random vector to represent parameters of uncertain values in a stochastic program. Most approaches to scenario generation are distribution-driven, that is, they attempt to construct a random vector which captures well in a probabilistic sense the uncertainty. On the other hand, a problem-driven approach may be able to exploit the structure of a problem to provide a more concise representation of the uncertainty. There have been only a few problem-driven approaches proposed, and these have been heuristic in nature.In this paper we propose what is, as far as we are aware, the first analytic approach to problem-driven scenario generation. This approach applies to stochastic programs with a tail risk measure, such as conditional value-at-risk. Since tail risk measures only depend on the upper tail of a distribution, standard methods of scenario generation, which typically spread there scenarios evenly across the support of the solution, struggle to adequately represent tail risk well. ",

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author = "Jamie Fairbrother and Amanda Turner and Wallace, {Stein W.}",

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T2 - an analytical approach for stochastic programs with tail risk measure

AU - Fairbrother, Jamie

AU - Turner, Amanda

AU - Wallace, Stein W.

PY - 2015/11

Y1 - 2015/11

N2 - Scenario generation is the construction of a discrete random vector to represent parameters of uncertain values in a stochastic program. Most approaches to scenario generation are distribution-driven, that is, they attempt to construct a random vector which captures well in a probabilistic sense the uncertainty. On the other hand, a problem-driven approach may be able to exploit the structure of a problem to provide a more concise representation of the uncertainty. There have been only a few problem-driven approaches proposed, and these have been heuristic in nature.In this paper we propose what is, as far as we are aware, the first analytic approach to problem-driven scenario generation. This approach applies to stochastic programs with a tail risk measure, such as conditional value-at-risk. Since tail risk measures only depend on the upper tail of a distribution, standard methods of scenario generation, which typically spread there scenarios evenly across the support of the solution, struggle to adequately represent tail risk well.

AB - Scenario generation is the construction of a discrete random vector to represent parameters of uncertain values in a stochastic program. Most approaches to scenario generation are distribution-driven, that is, they attempt to construct a random vector which captures well in a probabilistic sense the uncertainty. On the other hand, a problem-driven approach may be able to exploit the structure of a problem to provide a more concise representation of the uncertainty. There have been only a few problem-driven approaches proposed, and these have been heuristic in nature.In this paper we propose what is, as far as we are aware, the first analytic approach to problem-driven scenario generation. This approach applies to stochastic programs with a tail risk measure, such as conditional value-at-risk. Since tail risk measures only depend on the upper tail of a distribution, standard methods of scenario generation, which typically spread there scenarios evenly across the support of the solution, struggle to adequately represent tail risk well.

KW - math.OC

M3 - Journal article

JO - arxiv.org

JF - arxiv.org

ER -