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Approximate Uncertainty Modeling in Risk Analysis with Vine Copulas

Lookup NU author(s): Dr Kevin Wilson

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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.


Publication metadata

Author(s): Bedford T, Daneshkhah A, Wilson KJ

Publication type: Article

Publication status: Published

Journal: Risk Analysis

Year: 2016

Volume: 36

Issue: 4

Pages: 792-815

Print publication date: 01/04/2016

Online publication date: 02/09/2015

Acceptance date: 15/07/2015

Date deposited: 15/09/2015

ISSN (print): 0272-4332

ISSN (electronic): 1539-6924

Publisher: Wiley-Blackwell Publishing, Inc.

URL: http://dx.doi.org/10.1111/risa.12471

DOI: 10.1111/risa.12471

Notes: Article is Gold Open Access


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