Credibility Theory

Credibility theory prov1des us with techn1ques to determine insurance premiums for contracts that belong to a more or less heterogeneous portfolio, in case there is limited or irregular claims exper1ence for each contract but ample claims experience for the portfolio. It is the art and sc1ence of using both kinds of experience to adjust the insurance premiums and to improve their accuracy. The general and by now famous credibility formula C = (1 - Z) .B + Z.A originated in the United States during the years before World War I and was suggested in the field of workmen's compensation insurance. The industry- wide premium rate charged for a particular occupational class is represented by B. But an employer having a favourable record w1th this class tries to lower his premium to A, the rate based on his own experience. Because observat1ons of one employer are to a large extend ruled by random fluctuations, Whitney [1918) suggested a balance C between the two extremes A and B. Some 70 years ago he wrote: "The problem of experience rating arises out of the necess1ty , from the standpoint of equity to the individual risk , of stnk1ng a balance between class-experience on the one hand and risk exper1ence on the other" . It was felt that the mixing-factor Z should reflect the volume of the employer's experience. The larger this volume, the more credib1lity, by means of a high value of Z, is attached to the desired premium A. Thus it became common parlance to denote Z as "the credibility factor" or simply "the credibility". The theory of credibility 1s concerned w1th the quest1on of how much weight should be g1ven to th1s actual cla1ms experience. Of course , not only downward but also upward sh1fts 1n individual premiums are possible, although the employer's pressure 1n such cases will not be felt strongly.