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

116 Actuarial Modelling of Claim Counts
Crude claim rates 0.0695 0.0893 0.113 0.1325 0.1554
Figure 2.18
Map of Belgium with crude rates.
The approach however proceeds in two steps: first a regression is performed with all
the covariates except the spatial ones to get the expected claim number of each area, and
then the Boskov and Verrall model recovers the spatial claim pattern. In order to avoid the
preprocessing of the data to remove the effect of all risk factors other than the spatial ones,
Dimakos & Rattalma (2002) proposed a fully Bayesian approach to nonlife ratemaking.
This approach still relies on GLMs and thus suffers from the drawbacks mentioned in
Section 2.10.2: continuous covariates such as policyholders’ age enter linearly into the model
(on the score scale) whereas it is now well established that the effect of some continuous
variables is far from linear (typically, convex for policyholders’ age).
Statistical modelling tools to perform space-time analysis of insurance data have been
proposed by Denuit & Lang (2004) and Fahrmeir, Lang & Spies (2003). This approach
enables the actuary to explore spatial and temporal effects simultaneously with the impact
of other covariates. Bayesian generalized additive models provide a broad and flexible
framework for regression analyses in realistically complex situations with cross-sectional,
longitudinal and spatial data. All effects, as well as smoothing parameters, are regarded as
random and are assigned appropriate priors.
2.10.7 Software
SAS R has been used throughout this chapter. The readers interested in the use of this software
to perform statistical analyses are referred to Der & Everitt (2002) for a very readable