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#253




Finally started today, got through Mack this morning and now on Hurlimann. So far I'm not really a fan of the way CF does his outlines. I'd rather have the notation sprinkled in than in a list format, and he's super brief. Might just jump to the source now on Hurlimann and revisit CF after.
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ACAS 7 
#254




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#255




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To add a little bit to what you have already said, definitely use t*=√(p) unless otherwise stated. Also, remember to use the same value of t* for the relative MSE across all methods instead of changing it to match each method, i.e, only the credibility values change in the MSE formula (t, p, q are the same throughout). 
#256




The formulas for Hurlimann in CF are pissing me off and don't seem to make sense. Can you guys tell me what I'm misinterpreting?
Let's say you have a 4x4 triangle. The paper assumes that the reserve for the oldest year (year 1) should be 0 as it is at ultimate yes? But the way the formula is written for the reserve is R_i = Sum(S_i,k) from k = n  i +2 to k = n (apologies for notation). For the oldest row, that would imply the reserve should sum the incremental paid losses at periods 3 & 4, which doesn't make sense to me.
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ACAS 7 
#257




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I'll mention as an aside, that even though Hurlimann states this formula (page 83 of the source paper) it really doesn't seem to ever come into play in the actual calculations again when credibility is applied. I think CF just states it here for consistency. I skipped this formula altogether in my notes. 
#258




Shapland: Include process variance by replacing the future incremental losses with simulated values from a Gamma distribution. The gamma distribution is fit by setting
Variance = ϕ*(future incremental loss) Here's the part that confuses me. Shouldn't Variance = ϕ*(future incremental loss)^2 because the power z should be 2 under Gamma error? 
#259




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The assumption is that we are in the ODP model, which has z=1. So the mean is and the variance is . At this point, we are only considering parameter variance. To inject process variance, consider a gamma distribution with mean and variance . By sampling from this (simulating values for the incremental loss), we are considering a variety of possibilities while preserving the mean and standard deviation across simulations. This adds the process variance portion we need. Essentially, the Gamma distribution is a new assumption that is not inherent from the original ODP model. 
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