Dissertation
Higher Order Tail Dependence of Archimedean Copulas with Rapidly Varying Laplace Transforms
Doctor of Philosophy (PhD), Washington State University
01/2020
Handle:
https://hdl.handle.net/2376/108455
Abstract
It is well-known that Archimedean copulas with regularly varying Laplace transforms exhibit first-order tail dependence, an extremal dependence property, that is widely used in modeling and analysis, emerged from heavy tail phenomena. The lack of light tail analysis for Archimedean copulas, however, allows unacceptable data analysis in risk management and actuarial applications, where data sets exhibit higher order tail dependence hidden in sub-extremes. This dissertation fills this gap in tail dependence analysis of Archimedean copulas with rapidly varying Laplace transforms.
In this dissertation, we use the gamma family to model the Laplace transforms that generate Archimedean copulas, and quantitatively specify for the first time rapidly varying, light joint tails of Archimedean copulas. We then obtain the higher order tail dependence functions of Archimedean copulas with exponentially decaying tails. In comparison with Archimedean copulas with heavy tails, the sufficient conditions we obtained are rather mild. We also obtain the higher order tail dependence functions for several well-known copulas, such as Frank and Gumbel copulas. Our results complement the theory of tail dependence analysis of Archimedean copulas by providing higher order tail dependence analysis, in addition to the heavy tail dependence analysis, that is already available in the literature.
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Details
- Title
- Higher Order Tail Dependence of Archimedean Copulas with Rapidly Varying Laplace Transforms
- Creators
- Rui Huang
- Contributors
- Haijun Li (Advisor)Haijun Li (Committee Member)Hong-Ming Yin (Committee Member)Kevin R. Vixie (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Mathematics and Statistics, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Number of pages
- 83
- Identifiers
- 99900581810701842
- Language
- English
- Resource Type
- Dissertation