Remarks on the Swiss premium principle on positive risks
Abstract In this note it is proved that the Swiss premium principle is completely characterized by its premiums for positive Bernoulli risks. This yields another interpretation of the Swiss premium principle.
Positive homogeneity and multiplicativity of premium principles on positive risks
Abstract In this note it is shown that the Swiss premium principle on positive risks is, under a mild regularity condition, positively homogeneous or multiplicative if and only if it is the net premium principle. A similar result is obtained for a generalized form of the Orlicz principle.
A Rigorous Proof of a Property of the Premium Principle of Zero Utility in the Case of Additivity
A well-known theorem in risk theory states that a zero utility principle is additive if and only if it is the net premium principle or an exponential principle. However, the proof usually adopted in literature is incomplete. Therefore we give a new and rigorous proof using only simple mathematical tools.