Spring 2019 - Question #6 (Clark)

Hey All!

Regarding subject question.

I could be wrong, but sample 1 solution ignores the truncation point despite the fact that there is no development after 120 month. Is that correct?

Also sample 2 solution uses the adjustment when dealing with LDF method. For CC method, we deduct the result of growth function for each AY from the growth function result at truncation point (Clark - page 68). This is not how the sample 2 solution does it.

Am I missing something?

Hi!

Stepping back, the purpose of truncation is to only calculate the reserve up to a truncation point in the future. The reason is so that we don’t extrapolate too much into the tail of the G(x) distribution.

I would think of a truncation point like chopping off the G(x) curve at 120 months (in this problem).

For both the LDF and Cape Cod methods, the truncation point only comes into play when calculating the estimated reserve (part b of the problem). Everything else is done the same whether there’s truncation or not. In particular, we shouldn’t be taking truncation into account when calculating the expected incremental loss. These are incremental losses that happen before the truncation point anyway.

I like the Sample 1 solution for this problem the most. I think it better follows the paper. Sample 2 works as well, but does a bit of a workaround to adjust the G(X) curve for G(X_trunc) and andjust the ELR two. This basically cancels out in the calculation of the expected incremental losses and you end up with the same solution as Sample 1.

Below is a dropbox link for a workbook of the problem with some commentary on the truncation. I hope it helps!

Steve

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