Multivariate generalized Pareto distributions along extreme directions

Anas Mourahib, Anna Kiriliouk and Johan Segers
Additional contact information
Anas Mourahib: Université catholique de Louvain, LIDAM/ISBA, Belgium
Anna Kiriliouk: UNamur
Johan Segers: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2023034, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: When modeling a vector of risk variables, extreme scenarios are often of special interest. The peaks-over-thresholds method hinges on the notion that, asymptotically, the excesses over a vector of high thresholds follow a multivariate generalized Pareto distribution. However, existing literature has primarily concentrated on the setting when all risk variables are always large simultaneously. In reality, this assumption is often not met, especially in high dimensions. In response to this limitation, we study scenarios where distinct groups of risk variables may exhibit joint extremes while others do not. These discernible groups are derived from the angular measure inherent in the corresponding max-stable distribution, whence the term extreme direction. We explore such extreme directions within the framework of multivariate generalized Pareto distributions, with a focus on their probability density functions in relation to an appropriate dominating measure. Furthermore, we provide a stochastic construction that allows any prespecified set of risk groups to constitute the distribution’s extreme directions. This construction takes the form of a smoothed max-linear model and accommodates the full spectrum of conceivable max-stable dependence structures. Additionally, we introduce a generic simulation algorithm tailored for multivariate generalized Pareto distributions, offering specific implementations for extensions of the logistic and Hüsler–Reiss families capable of carrying arbitrary extreme directions.

Pages: 32
Date: 2023-11-09
New Economics Papers: this item is included in nep-ecm and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://dial.uclouvain.be/pr/boreal/en/object/bore ... tastream/PDF_01/view (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvad:2023034

Access Statistics for this paper

More papers in LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA) Voie du Roman Pays 20, 1348 Louvain-la-Neuve (Belgium). Contact information at EDIRC.
Bibliographic data for series maintained by Nadja Peiffer ().