Approximate Uncertainty Modeling in Risk Analysis with Vine Copulas.
Approximate Uncertainty Modeling in Risk Analysis with Vine Copulas.
复制标题
DOI：
10.1111/risa.12471
复制
发表时间：
2016-04
期刊：
影响因子：
--
通讯作者：
Wilson KJ
中科院分区：
文献类型：
--
作者：
Bedford T;Daneshkhah A;Wilson KJ
风险分析的许多应用要求我们联合建模多个不确定量。贝叶斯网络和copula是两种常用的建模方法与概率分布的联合不确定性。这篇文章的重点是通过发展库克，贝德福德，Kurowica和其他人在葡萄树上的工作，作为一种构建高维分布的方式，不受一些限制的替代品，如多元高斯copula的copula的新方法。这篇文章提供了一个基本的近似结果，表明我们可以近似任何密度，因为我们喜欢使用藤蔓。它进一步操作化这一结果，显示如何最小信息copula可以用来提供参数类的copula，有这样好的近似水平。我们扩展了以前的方法，考虑非恒定的条件依赖关系，这是特别相关的金融风险建模使用葡萄树。我们将讨论如何量化这些模型，在专家判断或拟合数据方面，并通过对两个金融数据集进行建模来说明这种方法。
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.