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

Fairbrother, Jamie and Turner, Amanda and Wallace, Stein W. (2015) Problem-driven scenario generation:an analytical approach for stochastic programs with tail risk measure. arxiv.org.

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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.

Item Type:
Journal Article
Journal or Publication Title:
arxiv.org
Subjects:
ID Code:
76971
Deposited By:
Deposited On:
02 Dec 2015 11:20
Refereed?:
No
Published?:
Published
Last Modified:
27 Nov 2020 02:49