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Generating scenario trees for multi-stage decision problems

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Generating scenario trees for multi-stage decision problems. / Hoyland, Kjetil; Wallace, Stein W.
In: Management Science, Vol. 47, No. 2, 02.2001, p. 295-307.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Hoyland, K & Wallace, SW 2001, 'Generating scenario trees for multi-stage decision problems', Management Science, vol. 47, no. 2, pp. 295-307. https://doi.org/10.1287/mnsc.47.2.295.9834

APA

Hoyland, K., & Wallace, S. W. (2001). Generating scenario trees for multi-stage decision problems. Management Science, 47(2), 295-307. https://doi.org/10.1287/mnsc.47.2.295.9834

Vancouver

Hoyland K, Wallace SW. Generating scenario trees for multi-stage decision problems. Management Science. 2001 Feb;47(2):295-307. doi: 10.1287/mnsc.47.2.295.9834

Author

Hoyland, Kjetil ; Wallace, Stein W. / Generating scenario trees for multi-stage decision problems. In: Management Science. 2001 ; Vol. 47, No. 2. pp. 295-307.

Bibtex

@article{28f500ae91a04d72a3b127a6842555a9,
title = "Generating scenario trees for multi-stage decision problems",
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.",
keywords = "Scenario Generation , Asset Allocation, Nonconvex Programming",
author = "Kjetil Hoyland and Wallace, {Stein W}",
year = "2001",
month = feb,
doi = "10.1287/mnsc.47.2.295.9834",
language = "English",
volume = "47",
pages = "295--307",
journal = "Management Science",
issn = "0025-1909",
publisher = "INFORMS Inst.for Operations Res.and the Management Sciences",
number = "2",

}

RIS

TY - JOUR

T1 - Generating scenario trees for multi-stage decision problems

AU - Hoyland, Kjetil

AU - Wallace, Stein W

PY - 2001/2

Y1 - 2001/2

N2 - 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.

AB - 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.

KW - Scenario Generation

KW - Asset Allocation

KW - Nonconvex Programming

U2 - 10.1287/mnsc.47.2.295.9834

DO - 10.1287/mnsc.47.2.295.9834

M3 - Journal article

VL - 47

SP - 295

EP - 307

JO - Management Science

JF - Management Science

SN - 0025-1909

IS - 2

ER -