Actuarial Modelling of Claim Counts Risk Classification, Credibility ...

Risk Classification 115
Raw exposure
(policyholders)
48 84 157 318 621
Figure 2.17
Map of Belgium with exposures-to-risk.
A key step in model specification is the definition of neighbours, i.e. those areas whose
claim rates are correlated with that of a given area. A traditional definition of neighbours
includes all areas contiguous to a given area. The methodology applied in Brouhns, Denuit,
Masuy & Verrall (2002) is as follows. In a first stage, available explanatory variables
are incorporated to the policyholders’ claim frequencies with the help of a (mixed) Poisson
regression model. In a second stage, the data are aggregated by districts and overdispersion
is accounted for by introduction of a random effect (split into a spatially structured part and
a spatially unstructured one). The Boskov and Verrall model is then used to recover the
spatial structure of the claims pattern that can be used to design the geographical ratemaking
strategy of the company.
In order to figure out the global claim pattern, Figure 2.19 displays the geographical
risk variation, and serves as basis for the determination of the rating areas. Clearly, several
regions with high, medium and low values of geographic risk emerge. This map can thus
serve to design different rating areas, which in turn become a categorical variable that may
enter the (mixed) Poisson regression model.