The Esscher Premium Principle: A Criticism

The Esscher premium principle has recently had some exposure, namely, with the works of BUHLMANN (1980) and GERBER (1980) BUHLMANN (1980) devised the principle and coined the name for it within the framework of utility theory and risk exchange. GERBER (1980), on the other hand, gives further insight into the principle by studying it within the realm of forecasting in much the same spirit as credibility theorists forecast premiums. However, there is an important distraction the choice of loss function. The present note sets out to criticize this relatively embryonic principle using decision theoretic arguments and indicates that the Esscher premium is essentially a small perturbation of the well established linearized credibility premium BOHLMANN (1970). Keywords: Credibility/Ex/Ind. Risk Rating Plans/Premium Analysis