Mate question #10 (From Bluhm chap 37)

Hi,



Is someone doing the Mate practice problem set ? In number 10, there are 4 different method to calculate the pooled loss ratios and redistribute claims.



What I dont understand is that under the credibility weighing and multi-year averaging method ( c) and d) ) if you multiply the pooled loss ratio with the actual premium you will not end up with the total claims before any pooling.



So basically ther are supposed to be methods to redistribute claims but you will not end up with the total claims before pooling.



If I try to create a simple example :



- Credibility Weighting method

- 2 groups

- Group 1 : 10 000 000 premium, 9 000 000 claims, 90% LR, 100% credible

- Group 2 : 1 000 000 premium, 500 000 claims, 50% LR, 0% credible

- Total : 11 000 000 premium, 9 500 000 claims, 86,36% LR



The pooled loss ratio under credibility method would then be:

- Group 1 : 90% LR

- Group 2 : 86,36% LR



Claims attributed to each group would be:

-Group 1 : 9 000 000

-Group 2 : 863 600

Total claims : $9 863 600 > $ 9 500 000



So we just gave $363 000 in claims to group 2 out of nowhere.



What am I missing here ?

Mate question #10 (From Bluhm chap 37)