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isaac218
04-23-2005, 07:42 PM
There is a problem related to Feldblum auto:

-30 policies terminate in the third year
-prob of termination in year 2 is 0.0816
-termination rate in year 2 is 0.100
-termination rate in year 3 is 0.075

a) calculate number of polices in year 1 and year 2
b) calculate the original number of policies in the cohort
c) calculate the termination rate prob of termination in year 1

My solution seems to work and I ended up doing it in a different order but I was wondering if anyone has tried this problem and got two different answers. Two of the main things to figure out are the termination rate in year 1 and the original number of polices.

For original # of policies I have 545 and for termination rate in year one I have .184
The exam solution gives 539 and .176 respectively

to check these points:

my solution: 545(1-.184)(1-.1)(.075) = 30
exam solution: 539(1-.176)(1-.1)(.075) = 30

my solution: 545(0.0816) = 545(1-.184)(0.100)
exam solution: 539(0.0816) =? 539(1-.176)(0.100)

Am I missing something? I think maybe I've been looking at it too hard. Any help would be appreciated.
Thanks

04-23-2005, 09:04 PM
Your answers are the same as Feldblums' answers on his study sheet. I'd go with Feldblum's answer (what you got) and not worry about an exam committe member who incorrectly solved a problem. Annoying, I know. But, somewhere in Feldblum's study notes, he mentions that the published essay questions are NOT necessarily correct. They are simply examples of essay anwers. Ridiculous, I know. Why would the CAS exam committe publish incorrect essay answers? Generally, if a an exam as an error in the soln one year, it does not the next, they don't admit to their mistakes, they just try not to repeat them.

isaac218
04-23-2005, 11:16 PM

Examinator
04-24-2005, 12:06 PM
If I remember correctly, the problem's discrepency came with rounding. When calculating the number of policies that persisted to the beginning of the second period, 400/0.900 = 444.444(etc.). The CAS sample answer rounded this to 444, leaving 44 to terminate in that second period (instead of 44.444). If you proceed with 44, you get the CAS solution. If you don't round anything, you get your solution (which is what I got too). I don't know if they round simply because we're talking about a discrete variable (number of policies), or what.

Would you assume that you could do it either way, document all assumptions, and get it right?

04-25-2005, 08:25 PM
If you method is correct, you show all work, but differ do to rounding, you should get full credit. I've hear two different advice techniques: 1. round to 3 decimal points-as most actuaries do in practice and 2. round to the same number of decimals (or digits) that are used in the question.

Colymbosathon ecplecticos
04-25-2005, 09:20 PM
round to 3 decimal points-as most actuaries do in practice

News to me!