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

90 Actuarial Modelling of Claim Counts
illustrations involving Portfolio A in the next chapters. The reason is that, in this case, explicit
expressions are available, providing a deeper insight in the mechanisms behind experience
rating systems.
2.8.2 Resulting Risk Classification for Portfolio A
Table 2.7 gives the resulting price list obtained with the Negative Binomial model of
Table 2.4. A ‘Yes’ indicates the presence of the characteristic corresponding to the column.
The final a priori ratemaking contains 23 classes. Table 2.7 gives the estimated expected
annual claim frequencies obtained from the Negative Binomial regression model, and the
relative importance of each risk class.
Note that there is another way to present the results displayed in Table 2.7. The idea is to
start from the annual expected claim frequency of the reference class, estimated to
exp̂ 0 = 1112 %
according to Table 2.4, and then to apply correction coefficients. Specifically, the annual
expected claim frequency of a given policyholder is simply obtained from
1112 %
⎧
exp06399 = 190 if the policyholder is a male aged between 18 and 24
⎪⎨
exp02363 = 127 if the policyholder is a female aged between 18 and 30
×
or a male aged between 25 and 30
⎪⎩
1
otherwise
{ exp−01805 = 083 if the policyholder lives in a rural district
×
1
otherwise
{ exp04783 = 161 if the policyholder splits the premium payment
×
1
otherwise
{ exp02145 = 124 if the policyholder uses the car for professional purposes
×
1
otherwise
2.9 Ratemaking using Panel Data
2.9.1 Longitudinal Data
Actuaries often pool several observation periods to determine the price list (the main goal
being to increase the size of the data base). The serial dependence arising from the fact that
the same individuals are followed and produce correlated claim numbers should prevent the
actuaries from using classical statistical techniques (which assume independence).
During the observation period, n policies have been in the portfolio, each one observed
during T i periods. Let N it be the number of claims reported by policyholder i during year t,
i = 1 2n, t = 1 2T i . Such motor insurance data have a panel structure: typically,
n is large whereas the T i s are small.
Let d it be the length of observation period t for policyholder i. Usually, d it = 1, but there
are a variety of situations where this is not the case. Indeed, a new period of observation