Approximate Uncertainty Modeling in Risk Analysis with Vine Copulas

Tim Bedford, Alireza Daneshkhah, Kevin Wilson

Research output: Contribution to journalArticlepeer-review

46 Citations (Scopus)
47 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)792-815
Number of pages23
JournalRisk Analysis
Issue number4
Early online date2 Sept 2015
Publication statusPublished - Apr 2016
Externally publishedYes

Bibliographical note

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium,
provided the original work is properly cited.


  • copula
  • Entropy
  • risk modelling
  • Pair-copula Construction
  • Information


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