Actuarial Outpost > CAS 2019 Exam 7 #6, part a: Contradiction with Clark Paper?
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#1
07-31-2020, 07:29 AM
 actuarialstudent89 CAS Join Date: Jan 2016 Studying for 7 College: American University Alumni Posts: 4
2019 Exam 7 #6, part a: Contradiction with Clark Paper?

Part a of this question states "Calculate the incremental fitted payment and corresponding normalized residual for accident year 2018 at 12 months using the Cape Cod method."

The examiner's report shows two sample solutions. Solution 1 uses the un-truncated growth function to calculate the used-up premium and ELR. And it sticks with this un-truncated growth function to find the expected incremental fitted payment.

Solution 2 is similarly consistent: using the truncated growth function throughout all calculations.

Although more logical, this contradicts the example provided in Clark, section 4.2. Clark uses the un-truncated growth function to calculate used-up premium, which is then used in calculating an ELR of 59.78%. However, he switches to the truncated version to calculate reserves. For example, AY 2000's growth function is 4.69%, but we instead use the truncated growth function (90.83% - 4.69%) to estimate reserves = 7,002,255 = 86.13%*[\$13.6M*59.78%]. The ELR of 59.78% corresponds to un-truncated values, but the 86.13% is derived using truncated values.

I guess I'll use the examiner's report method moving forward, but curious if anyone else has opinions on this.
#2
07-31-2020, 01:58 PM
 AbedNadir Member CAS SOA Join Date: Mar 2014 Studying for FCAS Posts: 2,877

it's interesting that the end result is the same, if you do the algebra you should see that things cancel out in the expected incremental calculation. looking at page 68 of Clarke for the CC reserve you also have (g(234)/g(234) - g(x)/g(234)) * ELR ( without truncation ) * g(234) * premium which is equal to the reserve they state. I guess this should be obvious since we already established the expected incrementals are the same under both methods.
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#3
08-01-2020, 05:32 AM
 actuarialstudent89 CAS Join Date: Jan 2016 Studying for 7 College: American University Alumni Posts: 4

Thanks for the response.

I think my misunderstanding is actually more basic: calculation of a fitted payment versus a reserve. In the case of a fitted payment, we do NOT consider truncation; truncation is only considered in the calculation of a reserve.