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#1




Challenge: 2017 Q10(a)  Bootstrapping and CY Trend
Here is the challenge:
Create a 6x6 triangle of incremental paid activity with a clear calendaryear trend such that, if you apply the bootstrap model process, you get residuals that resemble the solution in the examiners report. From http://www.casact.org/admissions/stu...exam7/177.pdf Quote:
Quote:

#2




I attempted this myself, but maybe I don't understand bootstrapping as well as I should.
I started with an oversimplified scenario where, for any accident year, 2000 is paid in year 1, then 1500, 1200, 1000, 700, and 400 for years 2, 3, 4, 5, 6. Then, I added a +10% calendar year trend by multiplying the second diagonal by 1.1, the third diagonal by 1.21, etc. This doesn't work at all, because the model just increases the agetoage factors by 10% and all residuals are zero. Alternatively, if you use a GLM approach where you don't allow gammas (or force all gammas to zero), your alphas and betas absorb the constant inflation and you get a perfect fit again. I introduced randomness, but that just gave me random residuals. I tried using increasing inflation (5%, 8%, 10%, 12%, 15% for CYs 2 through 6), and I got a Ushaped residuals graph. Decreasing inflation (15%, 12%, 10%, 8%, 5%) gave me a rainbowshaped graph. 
#3




I think the key words in the problem are: "due to
inflation which is not reflected in the model" What do you get if you recalculate the residuals where the fitted triangle is based on the triangle WITHOUT inflation? I tested this myself and got this: Last edited by Abelian Grape; 01022018 at 03:24 PM.. 
#4




Thanks for the response, Grape.
I agree that I must be misinterpreting the part of the question that you highlighted. I basically took it to mean "use a GLM approach but you're not allowed to use gammas". A few things though: 1. The "actuals with 10% inflation applied" should just be labeled "actuals", and your fit should be based on these. I don't think it makes sense to fit on something that didn't happen. 2. The sample solution starts with negative residuals at early CYs and goes to positive residuals for later CYs. 3. I don't think the bootstrap process will ever give materially nonzero residuals for the (1, 6) or (6, 1) coordinates. I follow your process, but I think it's too far removed from the syllabus bootstrap. 
#5




Quote:
2. I'll let you figure this one out. Hint: The topleft of the actuals triangle doesn't necessarily have to equal that of the fitted. 3. It will in the event that the fit doesn't capture something like inflation. 
#6




Quote:
Shapland has example files where he fits a GLM but does not allow CY parameters, but he doesn't have anything exactly like this problem. 
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