# Asymptotic independence and support detection techniques for heavy-tailed multivariate data

## TL;DR

This paper develops tools to identify asymptotic independence in heavy-tailed multivariate data, crucial for risk management, by analyzing dependence structures and estimating the support of the angular measure.

## Contribution

It introduces a consistent estimator for the support of the angular measure in multivariate regular variation, applicable in any dimension without prior support knowledge.

## Key findings

- Support estimator is asymptotically consistent.
- Supports rigorous testing via asymptotically normal test statistic.
- Method applies to any dimension N ≥ 2.

## Abstract

One of the central objectives of modern risk management is to find a set of risks where the probability of multiple simultaneous catastrophic events is negligible. That is, risks are taken only when their joint behavior seems sufficiently independent. This paper aims to help to identify asymptotically independent risks by providing additional tools for describing dependence structures of multiple risks when the individual risks can obtain very large values. The study is performed in the setting of multivariate regular variation. We show how asymptotic independence is connected to properties of the support of the angular measure and present an asymptotically consistent estimator of the support. The estimator generalizes to any dimension $N\geq 2$ and requires no prior knowledge of the support. The validity of the support estimate can be rigorously tested under mild assumptions by an asymptotically normal test statistic.