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

Risk Classification 101
These results are then corrected with a multiplying factor computed thanks to a Poisson
regression with ‘number of claims of the previous year’ as the single explanatory variable.
We use the sum of the logarithm of the estimated annual expected claim frequency obtained
when assuming serial independence and of the logarithm of the exposure-to-risk as an offset.
Specifically, the expected number of claims for policyholder i during period t, t = 2 3, is
now of the form
d it exp
(
̂0 +
)
p∑
̂j x itj exp˜ 0 +˜ 1 N it−1
j=1
where the ̂ j s are those of Table 2.10 and where the parameters ˜ 0 and ˜ 1 have to be
estimated by Poisson regression. The offset is
ln d it +̂ 0 +
p∑
̂j x itj
Results of the Poisson regression on the model incorporating the past claims are as follows:
j=1
Variable Coeff ˜ Std error Wald 95 % conf limit Chi-sq Pr>Chi-sq
Intercept −00412 00180 −0.0766 −00059 523 00222
N t−1 03241 00370 02517 03966 7688 Chi-sq
N t−1 1 68.66