Characterization Theorems for Scale Invariance Property of Insurance Premium Calculation Principles

Abstract

Characterization theorems for scale invariance property of insurance premium calculation principles are presented. Theorems formulated in a form of necessary and sufficient conditions for the mentioned property to be hold. Conditions are imposed on the auxiliary functions with the help of which several methods of pricing of insurance contracts are defined. Presented theorems cover cases of mean value, insurer equivalent utility, customer equivalent utility, and Swiss premium calculation principles. For mean value and customer zero utility premium calculation principles we present theorems demonstrating that in the case of pricing of only strictly positive risks, classes of the auxiliary functions producing scale invariant premiums are larger than in the general case.