Multivariate tail dependence and local stochastic dominance

TL;DR

This paper explores the relationship between tail dependence ordering and local stochastic dominance in multivariate copulas, revealing conditions under which they coincide, with implications for risk management.

Contribution

It establishes conditions where tail dependence orderings and local stochastic dominance align in multivariate copulas, including Archimedean and lower extreme value classes.

Findings

Tail dependence order and local stochastic dominance coincide for certain copula classes.

The results apply to risk management, enhancing understanding of dependence structures.

Not all tail dependence and stochastic dominance orders are equivalent in general.

Abstract

Given two multivariate copulas with corresponding tail dependence functions, we investigate the relation between a natural tail dependence ordering $\leq_{tdo}$ and the order $\leq_{loc}$ of local stochastic dominance. We show that, although the two orderings are not equivalent in general, they coincide for various important classes of copulas, among them all multivariate Archimedean and bivariate lower extreme value copulas. We illustrate the relevance of our results by an implication to risk management.