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

54 Actuarial Modelling of Claim Counts
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Figure 2.1 Exposure-to-risk in Portfolio A.
2.2.4 One-Way Analyses
Age
The age structure of the portfolio is described in Figure 2.2. Most policyholders are middleaged
as 6722 insured drivers (representing 46.4 % of the portfolio) are between 31 and 60.
Only 802 insured drivers (representing 5.8 % of the portfolio) are over 60. The young drivers
represent 15.3 % of the portfolio (2295 policyholders) and the remaining 4686 insured drivers
(32.5 % of the portfolio) are between 25 and 30.
In the preliminary descriptive analysis, the actuary considers the marginal impact of each
rating factor. The possible effect of the other explanatory variables is thus disregarded.
Let us assume for a while that the claim frequencies only depend on Age. If the
occurrence of the claims filed by the policyholders conforms with a Poisson process, the
number N i of claims reported by policholder i obeys the Poisson distribution with mean
d i Agei , where d i is the exposure-to-risk (i.e., the length of the coverage period) for
policyholder i, Agei is the age category to which policyholder i belongs (1, 2, 3 or
4) and the j s, j = 1 2 3 4, are the annual expected claim frequencies for the 4 age
classes.