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A Heuristic for Moment-Matching Scenario Generation

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Abstract

In stochastic programming models we always face the problem of how to represent the random variables. This is particularly difficult with multidimensional distributions. We present an algorithm that produces a discrete joint distribution consistent with specified values of the first four marginal moments and correlations. The joint distribution is constructed by decomposing the multivariate problem into univariate ones, and using an iterative procedure that combines simulation, Cholesky decomposition and various transformations to achieve the correct correlations without changing the marginal moments.

With the algorithm, we can generate 1000 one-period scenarios for 12 random variables in 16 seconds, and for 20 random variables in 48 seconds, on a Pentium III machine.

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Authors and Affiliations

  1. Gjensidige Nor Asset Management, P.O. Box 276, N-1326, Lysaker, Norway

    Kjetil Høyland

  2. Department of Industrial Economics and Technology Management, NTNU, N-7491, Trondheim, Norway

    Michal Kaut

  3. Molde University College, Servicebox 8, N-6405, Molde, Norway

    Stein W. Wallace

Authors
  1. Kjetil Høyland
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  2. Michal Kaut
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  3. Stein W. Wallace
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Høyland, K., Kaut, M. & Wallace, S.W. A Heuristic for Moment-Matching Scenario Generation. Computational Optimization and Applications 24, 169–185 (2003). https://doi.org/10.1023/A:1021853807313

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  • DOI: https://doi.org/10.1023/A:1021853807313

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