Extreme Negative Dependence and Risk Aggregation

TL;DR

This paper introduces the concept of extreme negative dependence (END) for sequences of random variables, providing a new benchmark for negative dependence, with applications to risk aggregation and bounds under dependence uncertainty.

Contribution

It defines and constructs END sequences, establishing their existence and properties, and applies these to derive bounds in risk aggregation problems.

Findings

END sequences always exist for finite mean marginals

END sequences control partial sums via a distribution-dependent variable

Asymptotic bounds for risk aggregation under dependence uncertainty

Abstract

We introduce the concept of an extremely negatively dependent (END) sequence of random variables with a given common marginal distribution. The END structure, as a new benchmark for negative dependence, is comparable to comonotonicity and independence. We show that an END sequence always exists for any given marginal distributions with a finite mean and we provide a probabilistic construction. Through such a construction, the partial sum of identically distributed but dependent random variables is controlled by a random variable that depends only on the marginal distribution of the sequence. The new concept and derived results are used to obtain asymptotic bounds for risk aggregation with dependence uncertainty.