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

236 Actuarial Modelling of Claim Counts
Table 5.5 Results of the LogNormal regression analysis for the claim costs recorded in Portfolio C.
Variable Level Coeff Std error Wald 95 % conf limit t-value Pr >t
Intercept 61223 00268 60702 61744 23038 60 01781 00312 01169 02392 571 Chi-sq
Ageph 2 4058 < .0001
City 1 770 0.0055
Agev 3 3820 < .0001
All the three remaining variables are statistically significant, and must be kept in the model.
5.2.6 Resulting Price List for Portfolio C
Formula for the Pure Premium
Let freq be the vector of the regression coefficient for the claim frequencies, that is,
the expected annual number of standard claims is exp freq
0 + ∑ p
j=1 freq j x ij . Similarly,
let cost be the regression coefficient for the moderate claim sizes. We retain here the
LogNormal modelling for the moderate claim sizes, so that the expected moderate claim
amount is exp cost
0
+ ∑ p
j=1 cost j
x ij + 2 /2. Neglecting the large claims, the pure premium
for policyholder i is given by
⎡ ⎤
Ni∑
small
(
p∑ (
E ⎣ C ik
⎦ = EN small
i
EC i1 = exp freq
0 + cost
0
+
freq
) )
j + cost
j xij + 2
2
k=1
If all the components of x i are binary, we then get a multiplicative price list. The total
premium is then obtained by adding the expected cost of the large losses, i.e. EN large
i EL i1 .
j=1