On the identification of the riskiest directional components from multivariate heavy-tailed data

TL;DR

This paper develops tools and algorithms to identify the riskiest directional components in multivariate heavy-tailed data, aiding risk assessment in insurance and finance by understanding dominant tail behaviors.

Contribution

It introduces consistent estimators for detecting dominating directions in multivariate heavy-tailed data, a novel approach for multivariate tail risk analysis.

Findings

Effective identification of riskiest directions in multivariate heavy tails

Estimators demonstrate consistency in high-dimensional settings

Applications in insurance and finance for risk management

Abstract

In univariate data, there exist standard procedures for identifying dominating features that produce the largest observations. However, in the multivariate setting, the situation is quite different. This paper aims to provide tools and algorithms for detecting dominating directional components in multivariate data. We study general heavy-tailed multivariate random vectors in dimension $d\geq 2$ and present consistent estimators which can be used to evaluate why the data is heavy-tailed. This is done by identifying the set of the riskiest directional components. The results are of particular interest in insurance when setting reinsurance policies and in finance when hedging a portfolio of multiple assets.