In this paper, we propose an analytic analogue to the simulation procedure described in Taylor (1997). We apply the formulas to a Belgian data set and discuss the interaction between a priori and a posteriori ratemakings.
Pitrebois, S., Walhin, J.-F., & Denuit, M. (2003). Setting a bonus-malus scale in the presence of other rating factors: Taylor’s work revisited. Astin Bulletin : the journal of the International Actuarial Association, 33, 419-436. https://doi.org/10.2143/AST.33.2.503701 (Original work published 2003)