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...

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...