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Correlations and Copulas for Decision and Risk Analysis

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Author Info

  • 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)

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    Abstract

    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.

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    File URL: http://dx.doi.org/10.1287/mnsc.45.2.208
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 45 (1999)
    Issue (Month): 2 (February)
    Pages: 208-224

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    Handle: RePEc:inm:ormnsc:v:45:y:1999:i:2:p:208-224

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    Related research

    Keywords: measures of dependence; Kendall's \tau ; Spearman's \rho ; copulas; multivariate normal copula; decision analysis process;

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    Cited by:
    1. Alexei Alexandrov & Özlem Bedre-Defolie, 2013. "The equivalence of bundling and advance sales," ESMT Research Working Papers ESMT-13-11, ESMT European School of Management and Technology.
    2. Hernández-Bastida, A. & Fernández-Sánchez, M.P. & Gómez-Déniz, E., 2009. "The net Bayes premium with dependence between the risk profiles," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 247-254, October.
    3. Chen, Songjiao & Wilson, William W. & Larsen, Ryan A. & Dahl, Bruce L., 2013. "Investing in Agriculture as an Asset Class," Agribusiness & Applied Economics Report 147053, North Dakota State University, Department of Agribusiness and Applied Economics.
    4. Stanhope, Stephen, 2005. "Case studies in multivariate-to-anything transforms for partially specified random vector generation," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 68-79, August.
    5. Penikas, Henry & Simakova, Varvara, 2009. "Interest Rate Risk Management Based on Copula-GARCH Models," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 13(1), pages 3-36.
    6. Penikas, H., 2010. "Financial Applications of Copula-Models," Journal of the New Economic Association, New Economic Association, issue 7, pages 24-44.
    7. Hammitt, James & Zhang, Yifan, 2012. "Combining Experts’ Judgments: Comparison of Algorithmic Methods using Synthetic Data," TSE Working Papers 12-293, Toulouse School of Economics (TSE).
    8. Michiels F. & De Schepper A., 2007. "A Copula Test Space Model: How To Avoid the Wrong Copula Choice," Working Papers 2007027, University of Antwerp, Faculty of Applied Economics.
    9. El Alaoui, Marwane & Benbachir, Saâd, 2012. "Spillover Effect in the MENA Area: Case of Four Financial Markets," MPRA Paper 48682, University Library of Munich, Germany.
    10. Agustín Hernández-Bastida & M. Fernández-Sánchez, 2012. "A Sarmanov family with beta and gamma marginal distributions: an application to the Bayes premium in a collective risk model," Statistical Methods and Applications, Springer, vol. 21(4), pages 391-409, November.
    11. Ilich, Nesa, 2009. "A matching algorithm for generation of statistically dependent random variables with arbitrary marginals," European Journal of Operational Research, Elsevier, vol. 192(2), pages 468-478, January.
    12. A. E. Ades & Karl Claxton & Mark Sculpher, 2006. "Evidence synthesis, parameter correlation and probabilistic sensitivity analysis," Health Economics, John Wiley & Sons, Ltd., vol. 15(4), pages 373-381.
    13. I-Tung Yang, 2006. "Using Gaussian copula to simulate repetitive projects," Construction Management and Economics, Taylor & Francis Journals, vol. 24(9), pages 901-909.
    14. van Dorp, J. Rene, 2005. "Statistical dependence through common risk factors: With applications in uncertainty analysis," European Journal of Operational Research, Elsevier, vol. 161(1), pages 240-255, February.
    15. Michal Kaut & Stein Wallace, 2011. "Shape-based scenario generation using copulas," Computational Management Science, Springer, vol. 8(1), pages 181-199, April.

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