Abstract
All theoretical premium principles, which use a utility function (such as exponential principle, mean value principle, zero utility principle, Swiss premium calculation principle, Orlicz principle, Esscher principle) are analyzed in the light of practical properties such as homogeneity (as usual for quota shares) and sub-additivity. It is proved that a theoretical premium principle, which fulfills only very weakened forms of both practical properties, reduces necessarily to the net premium principle. Therefore it is impossible that the principles and the properties above are reasonable simultaneously.
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