In this article, we characterize comonotonicity and related dependence structures among several random variables by the distribution of their sum. First we prove that if the sum has the same distribution as the corresponding comonotonic sum, then the underlying random variables must be...

When the dependence structure among several risks is unknown, it is common in the actuarial literature to study the worst dependence structure that gives rise to the riskiest aggregate loss. A central result is that the aggregate loss is the riskiest with respect to convex order when the...

It is well-known that if a random vector with given marginal distributions is comonotonic, it has the largest sum with respect to convex order. However, replacing the (unknown) copula by the comonotonic copula will in most cases not reflect reality well. For instance, in an insurance context we...

In this paper, we extend the concept of mutual exclusivity proposed by Dhaene and Denuit (1999) to its tail counterpart and baptise this new dependency structure as tail mutual exclusivity. Probability levels are first specified for each component of the random vector. Under this dependency...