Asymptotic independence in higher dimensions and its implications on risk management
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911174719700992 |
|---|---|
| author | Das, Bikramjit Fasen-Hartmann, Vicky |
| author_facet | Das, Bikramjit Fasen-Hartmann, Vicky |
| contents | In the study of extremes, the presence of asymptotic independence signifies that extreme events across multiple variables are probably less likely to occur together. Although well-understood in a bivariate context, the concept remains relatively unexplored when addressing the nuances of the joint occurrence of extremes in higher dimensions. In this paper, we propose a notion of mutual asymptotic independence to capture the behavior of joint extremes in dimensions larger than two and contrast it with the classical notion of (pairwise) asymptotic independence. Additionally, we define k-wise asymptotic independence, which captures the tail dependence between pairwise and mutual asymptotic independence. The concepts are compared using examples of Archimedean, Gaussian and Marshall-Olkin copulas, among others. Finally, we discuss the implications of these new notions of asymptotic independence on assessing the risk of complex systems under distributional ambiguity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19186 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic independence in higher dimensions and its implications on risk management Das, Bikramjit Fasen-Hartmann, Vicky Statistics Theory Primary 62H05, 62H20, 62E20, Secondary 62G32, 62P05 In the study of extremes, the presence of asymptotic independence signifies that extreme events across multiple variables are probably less likely to occur together. Although well-understood in a bivariate context, the concept remains relatively unexplored when addressing the nuances of the joint occurrence of extremes in higher dimensions. In this paper, we propose a notion of mutual asymptotic independence to capture the behavior of joint extremes in dimensions larger than two and contrast it with the classical notion of (pairwise) asymptotic independence. Additionally, we define k-wise asymptotic independence, which captures the tail dependence between pairwise and mutual asymptotic independence. The concepts are compared using examples of Archimedean, Gaussian and Marshall-Olkin copulas, among others. Finally, we discuss the implications of these new notions of asymptotic independence on assessing the risk of complex systems under distributional ambiguity. |
| title | Asymptotic independence in higher dimensions and its implications on risk management |
| topic | Statistics Theory Primary 62H05, 62H20, 62E20, Secondary 62G32, 62P05 |
| url | https://arxiv.org/abs/2406.19186 |