Measuring sensitivity in a bonus–malus system

In performing Bayesian analysis of a bonus–malus system (BMS) it is normal to choose a parametric structure, π0(λ), in the insurer’s portfolio. According to Bayesian sensitivity analysis the structure function can be modelled by specifying a class Γ of priors instead of a single prior. In this paper, we examine the ranges of the relativities, i.e. δπ=E[λπ(λ|data)]/E[λπ(λ)], π∈Γ. We illustrate our method with data from [Astin Bulletin 10 (3) (1979) 274].