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Generating scenario trees for multi-stage decision problems

Hoyland, Kjetil and Wallace, Stein W (2001) Generating scenario trees for multi-stage decision problems. Management Science, 47 (2). pp. 295-307. ISSN 0025-1909

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    Abstract

    In models of decision making under uncertainty we often are faced with the problem of representing the uncertainties in a form suitable for quantitative models. If the uncertainties are expressed in terms of multivariate continuous distributions, or a discrete distribution with far too many outcomes, we normally face two possibilities: either creating a decision model with internal sampling, or trying to find a simple discrete approximation of the given distribution that serves as input to the model. This paper presents a method based on nonlinear programming that can be used to generate a limited number of discrete outcomes that satisfy specified statistical properties. Users are free to specify any statistical properties they find relevant, and the method can handle inconsistencies in the specifications. The basic idea is to minimize some measure of distance between the statistical properties of the generated outcomes and the specified properties. We illustrate the method by single- and multiple-period problems. The results are encouraging in that a limited number of generated outcomes indeed have statistical properties that are close to or equal to the specifications. We discuss how to verify that the relevant statistical properties are captured in these specifications, and argue that what are the relevant properties, will be problem dependent.

    Item Type: Article
    Journal or Publication Title: Management Science
    Uncontrolled Keywords: Scenario Generation ; Asset Allocation ; Nonconvex Programming
    Subjects:
    Departments: Lancaster University Management School > Management Science
    ID Code: 45383
    Deposited By: ep_importer_pure
    Deposited On: 11 Jul 2011 19:31
    Refereed?: Yes
    Published?: Published
    Last Modified: 26 Jul 2012 19:15
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/45383

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