Approximate uncertainty modeling in risk analysis with vine copulas

Tim Bedford, Alireza Daneshkhah, Kevin J. Wilson

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)
118 Downloads (Pure)


Many applications of risk analysis require us to jointly model multiple uncertain quantities. Bayesian networks and copulas are two common approaches to modelling joint uncertainties with probability distributions. This paper 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 which do not suffer from some of the restrictions of alternatives such as the multivariate Gaussian copula. The paper 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 which have such good levels of approximation. We extend previous approaches using vines by considering non-constant conditional dependencies which are particularly relevant in financial risk modelling. We discuss how such models may be quantified, in terms of expert judgement or by fitting data, and illustrate the approach by modelling two financial datasets.
Original languageEnglish
Pages (from-to)792-815
Number of pages24
JournalRisk Analysis
Issue number4
Early online date2 Sept 2015
Publication statusPublished - 30 Apr 2016


  • risk analysis
  • risk modelling
  • Bayesian networks
  • copula
  • entropy
  • vines


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