Comonotonicity, correlation order and premium principles

In this paper, we investigate the notion of dependency between risks and its effect on the related stop-loss premiums. The concept of comonotonicity, being an extreme case of dependency, is discussed in detail. For the bivariate case, it is shown that, given the distributions of the individual risks, comonotonicity leads to maximal stop-loss premiums. Some properties of stop-loss preserving premium principles are considered. A simple proof is given for the sub-additivity property of Wangʹs premium principle.