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Approximate Uncertainty Modeling in Risk Analysis with Vine Copulas


  • Tim Bedford
  • Alireza Daneshkhah
  • Kevin J. Wilson


Many applications of risk analysis require us to jointly model multiple uncertain quantities. Bayesian networks and copulas are two common approaches to modeling joint uncertainties with probability distributions. This article focuses on new methodologies for copulas by developing work of Cooke, Bedford, Kurowica, and others on vines as a way of constructing higher dimensional distributions that do not suffer from some of the restrictions of alternatives such as the multivariate Gaussian copula. The article provides a fundamental approximation result, demonstrating that we can approximate any density as closely as we like using vines. It further operationalizes this result by showing how minimum information copulas can be used to provide parametric classes of copulas that have such good levels of approximation. We extend previous approaches using vines by considering nonconstant conditional dependencies, which are particularly relevant in financial risk modeling. We discuss how such models may be quantified, in terms of expert judgment or by fitting data, and illustrate the approach by modeling two financial data sets.

Suggested Citation

  • Tim Bedford & Alireza Daneshkhah & Kevin J. Wilson, 2016. "Approximate Uncertainty Modeling in Risk Analysis with Vine Copulas," Risk Analysis, John Wiley & Sons, vol. 36(4), pages 792-815, April.
  • Handle: RePEc:wly:riskan:v:36:y:2016:i:4:p:792-815
    DOI: 10.1111/risa.12471

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    References listed on IDEAS

    1. Mohamed N. Jouini & Robert T. Clemen, 1996. "Copula Models for Aggregating Expert Opinions," Operations Research, INFORMS, vol. 44(3), pages 444-457, June.
    2. Ali E. Abbas, 2009. "Multiattribute Utility Copulas," Operations Research, INFORMS, vol. 57(6), pages 1367-1383, December.
    3. Bahar Biller, 2009. "Copula-Based Multivariate Input Models for Stochastic Simulation," Operations Research, INFORMS, vol. 57(4), pages 878-892, August.
    4. Frahm, Gabriel & Junker, Markus & Schmidt, Rafael, 2005. "Estimating the tail-dependence coefficient: Properties and pitfalls," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 80-100, August.
    5. Terje Aven, 2010. "On the Need for Restricting the Probabilistic Analysis in Risk Assessments to Variability," Risk Analysis, John Wiley & Sons, vol. 30(3), pages 354-360, March.
    6. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    7. Ali E. Abbas & David V. Budescu & Yuhong (Rola) Gu, 2010. "Assessing Joint Distributions with Isoprobability Contours," Management Science, INFORMS, vol. 56(6), pages 997-1011, June.
    8. Acar, Elif F. & Genest, Christian & Nešlehová, Johanna, 2012. "Beyond simplified pair-copula constructions," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 74-90.
    9. Terje Aven, 2010. "Reply to Discussants on “The Need for Restricting the Probabilistic Analysis in Risk Assessments to Variability”," Risk Analysis, John Wiley & Sons, vol. 30(3), pages 381-384, March.
    10. Emanuele Borgonovo, 2008. "Epistemic Uncertainty in the Ranking and Categorization of Probabilistic Safety Assessment Model Elements: Issues and Findings," Risk Analysis, John Wiley & Sons, vol. 28(4), pages 983-1001, August.
    11. Robert T. Clemen & Terence Reilly, 1999. "Correlations and Copulas for Decision and Risk Analysis," Management Science, INFORMS, vol. 45(2), pages 208-224, February.
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    Cited by:

    1. Wang, Zhonglai & Liu, Jing & Yu, Shui, 2020. "Time-variant reliability prediction for dynamic systems using partial information," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    2. Christoph Werner & Tim Bedford & John Quigley, 2018. "Sequential Refined Partitioning for Probabilistic Dependence Assessment," Risk Analysis, John Wiley & Sons, vol. 38(12), pages 2683-2702, December.

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