ABSTRACT
A standard premium principle (as least from a theoretical point of view) is the expected value principle: the premium associated to some (annual) risk S is pi(S) = (1 + α)E(S), where α > 0 denotes some loading, and where S is the annual random loss. Let (Nt) be the count process that denotes the number of claims occurred during period [0, t]. Let (Yi) denote the amount of the ith claim. Then the total loss over period [0, t] is
St =
Yi with St = 0 if Nt = 0.
