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Approximate Uncertainty Modeling in Risk Analysis with Vine Copulas
Tim Bedford1, Alireza Daneshkhah2, Kevin J Wilson1
1Department of Management Science, University of Strathclyde, Glasgow, UK.
Risk Analysis : an Official Publication of the Society for Risk Analysis
|September 3, 2015
Summary
This study introduces novel vine-based copula methods for joint uncertainty modeling in risk analysis. These methods offer superior approximation capabilities for complex, high-dimensional probability distributions, especially with non-constant dependencies.
Area of Science:
- Probability theory
- Statistical modeling
- Risk analysis
Background:
- Jointly modeling multiple uncertain quantities is crucial for risk analysis.
- Bayesian networks and copulas are standard methods for this, but have limitations.
Purpose of the Study:
- To develop new methodologies for copulas using vine structures.
- To address limitations of existing approaches like the multivariate Gaussian copula.
Main Methods:
- Utilizing vine structures for constructing higher-dimensional probability distributions.
- Applying minimum information copulas for parametric approximation.
- Extending vine methods to include non-constant conditional dependencies.
Main Results:
- Demonstrated a fundamental approximation result: any density can be closely approximated using vines.
- Developed parametric copula classes with strong approximation properties.
- Showcased applicability to financial risk modeling with non-constant dependencies.
Conclusions:
- Vine-based copulas provide a flexible and powerful framework for joint uncertainty modeling.
- The proposed methods enhance the approximation of complex probability distributions.
- These techniques are valuable for financial risk analysis and can be quantified via expert judgment or data fitting.
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