Please help! ASM PE 2, #19

[Evi]

19.
For each exposure in a group, the hypothetical mean of aggregate losses is theta and the process variance is exp(.3*theta). Theta varies by exposure and follows an exponential distribution with mean 3.

For three years experience from a group, you have the following data:

Year Exposures Aggregate losses
1 20 70
2 25 90
3 30 110

There will be 35 exposures in the group next year. Calculate the Buhlmann-Straub credibility premium

So I got a=10, v=9. But then I noticed that theta varies by exposure, not group. So why would information about different people give information about the 35 people in the group next year (who may or may not be the same people from last year)? Since we are not told that the mean varies by group, we should assume that the mean is the same for any group, and so a=0, and the credibility is 0.

[dawes]

I think since it varies by exposure, you would calculate the credibility for a single exposure, (ie. n = 20 + 25 + 30 = 75), then multiply the end result by 35 for the group next year.

P.S. I believe you have your a and v mixed up. I just did it and got the correct answer. u = 3, a = 9, v = 10, n = 75.

[Abraham Weishaus]

I agree that the question is defective. I should've said that θ varies by group, not by exposure.

[Evi]

Sorry, I meant a=9, v=10.