Setting a Bonus-Malus Scale in the Presence of Other Rating Factors

The operation of a bonus-malus system, superimposed on a premium system involving a number of other rating variables, is considered. To the extent that good risks are rewarded in their base premiums, through the other rating variables, the size of the bonus they require for equity is reduced. The issue is discussed quantitatively, and a numerical example is given. Keywords: Bonus-malus, experience rating.