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

250 Actuarial Modelling of Claim Counts
Hence, the expected number of moderate accidents is given by
EM small
i
= ˜ i =
i
PrCA i1 >RL i l i =
i
(
1 − − )
i −
√ i
2 + 2
The expected annual number of minor accidents ˜ i caused by policyholder i in Portfolio C
are displayed in Table 5.14.
The total number of accidents M i caused by policyholder i is then equal to
M i = M small
i
+ N large
i
since all the major accidents are reported to the company. The actual number of claims
originating from the M i accidents is
N i = N small
i
+ N large
i
Table 5.14 Expected annual claim frequency and corresponding expected annual
accident frequency for the different risk classes in Portfolio C.
Risk class Claim frequency Accident frequency
18–24 + Rural + 0–2 0.3513403 03633521
18–24 + Rural + 3–5 0.3301527 03517856
18–24 + Rural + 6–10 0.3513403 03824574
18–24 + Rural+>10 0.3513403 03777624
18–24 + Urban + 0–2 0.4408723 04572087
18–24 + Urban + 3–5 0.4142855 04435002
18–24 + Urban + 6–10 0.4408723 04827648
18 − 24 + Urban+>10 0.4408723 04765034
>60 + Rural + 0–2 0.1476220 01659192
>60 + Rural + 3–5 0.1387197 01683992
>60 + Rural + 6–10 0.1476220 0188461
>60 + Rural+>10 0.1476220 01831299
>60 + Urban + 0–2 0.1852406 0209793
>60 + Urban + 3–5 0.1740696 02137084
>60 + Urban + 6–10 0.1852406 02396818
>60 + Urban+>10 0.1852406 02326217
25–60 + Rural + 0–2 0.1845933 01964037
25–60 + Rural + 3–5 0.1734614 0193623
25–60 + Rural + 6–10 0.1845933 02129273
25–60 + Rural+>10 0.1845933 0208954
25–60 + Urban + 0–2 0.2316332 02475869
25–60 + Urban + 3–5 0.2176646 02447353
25–60 + Urban + 6–10 0.2316332 02695796
25–60 + Urban+>10 0.2316332 0264303