In this article, we show that some important implications concerning comonotonic couples and corresponding convex order relations for their sums cannot be translated to counter-monotonicity in general. In a financial context, it amounts to saying that merging counter-monotonic positions does not...

In this paper, we characterize counter-monotonic and upper comonotonic random vectors by the optimality of the sum of their components in the senses of the convex order and tail convex order respectively. In the first part, we extend the characterization of comonotonicity by  Cheung (2010) and...

Mutual exclusivity is an extreme negative dependence structure that was first proposed and studied in Dhaene and Denuit (1999) in the context of insurance risks. In this article, we revisit this notion and present versatile characterizations of mutually exclusive random vectors via their...

The determination of the dependence structure giving rise to the minimal convex sum in a general Fréchet space is a practical, yet challenging problem in quantitative risk management. In this article, we consider the closely related problem of finding lower bounds on three kinds of convex...

It is well known that if a random vector with given marginal distributions is comonotonic, it has the largest sum with respect to the convex order. In this paper, we prove that the converse is also true, provided that each marginal distribution is continuous.

In this paper, we study stochastic orders of scalar products of random vectors. Based on the study of Ma [Ma, C., 2000. Convex orders for linear combinations of random variables. J. Statist. Plann. Inference 84, 11-25], we first obtain more general conditions under which linear combinations of...

In this paper, we study the problems of optimal allocation of policy limits and deductibles. Several objective functions are considered: maximizing the expected utility of wealth assuming the losses are independent, minimizing the expected total retained loss and maximizing the expected utility...