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...

We investigate the influence of the dependence between random losses on the shortfall and on the diversification benefit that arises from merging these losses. We prove that increasing the dependence between losses, expressed in terms of correlation order, has an increasing effect on the...

Using a standard reduction argument based on conditional expectations, this paper argues that risk sharing is always beneficial (with respect to convex order or second degree stochastic dominance) provided the risk-averse agents share the total losses appropriately (whatever the distribution of...

Comonotonicity provides a convenient convex upper bound for a sum of random variables with arbitrary dependence structure. Improved convex upper bound was introduced via conditioning by Kaas et al. [Kaas, R., Dhaene, J., Goovaerts, M., 2000. Upper and lower bounds for sums of random variables....

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.