  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.
