On distribution-free safe layer-additive pricing

It is shown that a distribution-free implicit price loading method, which sets prices using a modified Hardy-Littlewood majorant of the stop-loss ordered maximal random variable by given range, mean and variance, induces distribution-free safe layer-additive distortion pricing. As a by-product, Karlsruhe pricing turns out to be a valid linear approximation to Hardy-Littlewood pricing in case the coefficient of variation is sufficiently high.