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Correlations and Copulas for Decision and Risk Analysis


  • Robert T. Clemen

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

  • Terence Reilly

    (Division of Math and Sciences, Babson College, Babson Park, Massachusetts 02157)


The construction of a probabilistic model is a key step in most decision and risk analyses. Typically this is done by defining a joint distribution in terms of marginal and conditional distributions for the model's random variables. We describe an alternative approach that uses a copula to construct joint distributions and pairwise correlations to incorporate dependence among the variables. The approach is designed specifically to permit the use of an expert's subjective judgments of marginal distributions and correlations. The copula that underlies the multivariate normal distribution provides the basis for modeling dependence, but arbitrary marginals are allowed. We discuss how correlations can be assessed using techniques that are familiar to decision analysts, and we report the results of an empirical study of the accuracy of the assessment methods. The approach is demonstrated in the context of a simple example, including a study of the sensitivity of the results to the assessed correlations.

Suggested Citation

  • Robert T. Clemen & Terence Reilly, 1999. "Correlations and Copulas for Decision and Risk Analysis," Management Science, INFORMS, vol. 45(2), pages 208-224, February.
  • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:2:p:208-224
    DOI: 10.1287/mnsc.45.2.208

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    References listed on IDEAS

    1. Robert L. Winkler & Wayne S. Smith & Ram B. Kulkarni, 1978. "Adaptive Forecasting Models Based on Predictive Distributions," Management Science, INFORMS, vol. 24(10), pages 977-986, June.
    2. Donald L. Keefer & Samuel E. Bodily, 1983. "Three-Point Approximations for Continuous Random Variables," Management Science, INFORMS, vol. 29(5), pages 595-609, May.
    3. Woojune Yi & Vicki M. Bier, 1998. "An Application of Copulas to Accident Precursor Analysis," Management Science, INFORMS, vol. 44(12-Part-2), pages 257-270, December.
    4. Donald L. Keefer, 1994. "Certainty Equivalents for Three-Point Discrete-Distribution Approximations," Management Science, INFORMS, vol. 40(6), pages 760-773, June.
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