Theoretical principles of premium calculation
Insurance Mathematics

A premium calculation principle is a mathematical function which, for a risk X, associates the corresponding technical premium Π(X), the sum of the pure premium and the technical loading. The choice of a premium calculation principle is a matter for the insurer, in particular the manager of the risk group concerned. This choice depends in particular on the latter's attitude to risk, especially in the case of large risks.

By $\mathcal{R}$ we mean the set of risks, i.e. the set of positive or zero random variables, and by