# Conditional Tail Independence in Archimedean Copula Models

## TL;DR

This paper demonstrates that in Archimedean copula models, the conditional distribution of a vector given one component exhibits tail independence under mild conditions, regardless of the overall tail behavior, with extensions to Archimax copulas.

## Contribution

It reveals a new tail independence property in Archimedean and Archimax copulas under mild generator conditions.

## Key findings

- Conditional distributions have independent upper tails.
- Tail independence holds regardless of unconditional tail behavior.
- Results extend to Archimax copulas.

## Abstract

Consider a random vector $U$, whose distribution function coincides in its upper tail with that of an Archimedean copula. We report the fact that the conditional distribution of $U$, conditional on one of its components, has under a mild condition on the generator function independent upper tails, no matter what the unconditional tail behavior is. This finding is extended to Archimax copulas.