Distribution-free comparison of pricing principles

Given the mean, coefficient of variation and finite range of a risk, we determine the stop-loss ordered extremal prices for four plausible pricing principles, namely the exponential principle, a new truncated linear zero-utility principle, the PH-transform principle and the Dutch principle. If in the extreme situation of a maximum coefficient of variation, the price of a risk should be maximum and uniquely defined, then the obtained distribution-free prices can be made parameter-free and compared. It is shown that the maximum distribution-free truncated linear zero-utility prices coincide with the minimum distribution-free PH-transform and Dutch prices.