Tail copula representation of path-based maximal tail dependence
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918432303218688 |
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| author | Koike, Takaaki Hofert, Marius Tsunekawa, Haruki |
| author_facet | Koike, Takaaki Hofert, Marius Tsunekawa, Haruki |
| contents | The classical tail dependence coefficient (TDC) may fail to capture non-exchangeable features of tail dependence due to its restrictive focus on the diagonal of the underlying copula. To address this limitation, the framework of path-based maximal tail dependence has been proposed, where a path of maximal dependence is derived to capture the most pronounced feature of dependence over all possible paths, and the path-based maximal TDC serves as a natural analogue of the classical TDC along this path. However, the theoretical foundations of path-based tail analyses, in particular the existence and analytical tractability, have remained limited. This paper addresses this issue in several ways. First, we prove the existence of a path of maximal dependence and the path-based maximal TDC when the underlying copula admits a non-degenerate tail copula. Second, we obtain an explicit characterization of the maximal TDC in terms of the tail copula. Third, we show that the first-order asymptotics of a path of maximal dependence is characterized by a one-dimensional optimization involving the tail copula. These results improve the analytical and computational tractability of path-based tail analyses. As an application, we derive the asymptotic behavior of a path of maximal dependence for the bivariate t-copula and the survival Marshall--Olkin copula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05985 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tail copula representation of path-based maximal tail dependence Koike, Takaaki Hofert, Marius Tsunekawa, Haruki Risk Management The classical tail dependence coefficient (TDC) may fail to capture non-exchangeable features of tail dependence due to its restrictive focus on the diagonal of the underlying copula. To address this limitation, the framework of path-based maximal tail dependence has been proposed, where a path of maximal dependence is derived to capture the most pronounced feature of dependence over all possible paths, and the path-based maximal TDC serves as a natural analogue of the classical TDC along this path. However, the theoretical foundations of path-based tail analyses, in particular the existence and analytical tractability, have remained limited. This paper addresses this issue in several ways. First, we prove the existence of a path of maximal dependence and the path-based maximal TDC when the underlying copula admits a non-degenerate tail copula. Second, we obtain an explicit characterization of the maximal TDC in terms of the tail copula. Third, we show that the first-order asymptotics of a path of maximal dependence is characterized by a one-dimensional optimization involving the tail copula. These results improve the analytical and computational tractability of path-based tail analyses. As an application, we derive the asymptotic behavior of a path of maximal dependence for the bivariate t-copula and the survival Marshall--Olkin copula. |
| title | Tail copula representation of path-based maximal tail dependence |
| topic | Risk Management |
| url | https://arxiv.org/abs/2604.05985 |