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

Research output: Contribution to journalJournal article

E-pub ahead of print
<mark>Journal publication date</mark>11/2015
<mark>Journal</mark>arxiv.org
Publication statusE-pub ahead of print
Original languageEnglish

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.