Experience Rating A New Application of the Collective Theory of Risk*)

Besides its well known applications, the collective risk theory has recently also been applied to problems connected with the so called Experience Rating. This term is used to define a method of premium calculation in insurance business which is based partially or totally on the individual experience of the particular risk involved. It is obvious that Experience Rating is essentially applicable to collective insurances which contain no saving element. In practical applications various possibilities may be considered.The collective theory of risk provides an efficient calculus for the analysis of the various forms of Experience Rating and in paper [3] a particular form of Experience Rating for collective insurances is examined. It is there assumed that the collective risk premium is based on experience derived from non-individual observations. If any cost loading is disregarded, the net premium is given by the relation P′ = (I + λ) P, where λ is a security factor and P the part of the premium covering the expected claims cost.A premium refund is to be deducted from the basic net premium P′. In this formula α′ and β are suitable numerical values and S means the due sum to be paid out for claims. Hence the net cost to the group considered depends on the actual claims S and therefore takes into account the individual claims experience. It may be shown that for β = I the form of Experience Rating considered is equivalent to a stop loss cover. The general case with β ≠I represents a combination of ordinary insurance cover and stop loss cover.