Living on the multi-dimensional edge: seeking hidden risks using regular variation

TL;DR

This paper introduces a more flexible definition of hidden regular variation to improve tail risk estimation in multivariate settings across various fields.

Contribution

It proposes an enhanced framework for hidden regular variation, enabling more accurate risk estimates for complex tail regions beyond classical models.

Findings

Improved risk estimates for a broader class of tail regions

Enhanced accuracy over classical regular variation models

Applicable across finance, insurance, and environmental science

Abstract

Multivariate regular variation plays a role assessing tail risk in diverse applications such as finance, telecommunications, insurance and environmental science. The classical theory, being based on an asymptotic model, sometimes leads to inaccurate and useless estimates of probabilities of joint tail regions. This problem can be partly ameliorated by using hidden regular variation [Resnick, 2002, Mitra and Resnick, 2010]. We offer a more flexible definition of hidden regular variation that provides improved risk estimates for a larger class of risk tail regions.