Approximate Uncertainty Modeling in Risk Analysis with Vine Copulas

Risk Analysis : an Official Publication of the Society for Risk Analysis
Tim BedfordKevin J Wilson

Abstract

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.

References

Jun 17, 2008·Risk Analysis : an Official Publication of the Society for Risk Analysis·Emanuele Borgonovo
Nov 19, 2009·Risk Analysis : an Official Publication of the Society for Risk Analysis·Terje Aven

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Citations

Aug 9, 2018·Risk Analysis : an Official Publication of the Society for Risk Analysis·Christoph WernerJohn Quigley
Jul 25, 2020·Journal of Bioinformatics and Computational Biology·O ChatrabgounA Daneshkhah
May 12, 2021·Royal Society Open Science·Maximilian ZellnerAram Galstyan

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Software Mentioned

R
Matlab
VineCopula
R package
NORTA
FMINSEARCH

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