Credibility and univariate classification

[TheZaha]

so in the W/M appendix they have a univariate classification example using 1) pure premium approach and 2) loss ratio approach and both apply credibility to change in relativity for each class, where the complement is no change.

in the pure premium method, the credibility is applied to a normalized relativity (i.e. relative to total not base) but in the loss ratio appraoch no normalization appears to be required. Does anyone know why it must be normalized for pure premium approach but not for loss ratio? When i was doing problems I normalized everything which appeared to be incorrect for the loss ratio problems.

Any and all help appreciated!

[actuarialista]

so in the W/M appendix they have a univariate classification example using 1) pure premium approach and 2) loss ratio approach and both apply credibility to change in relativity for each class, where the complement is no change.

in the pure premium method, the credibility is applied to a normalized relativity (i.e. relative to total not base) but in the loss ratio appraoch no normalization appears to be required. Does anyone know why it must be normalized for pure premium approach but not for loss ratio? When i was doing problems I normalized everything which appeared to be incorrect for the loss ratio problems.

Any and all help appreciated!

Zaha, in your first paragraph you seem to be saying that on W/M Page E-3 (pure prem method) they take a credibility-weighting of the change in relativity. To me it looks like the are credibility-weighting the normalized indicated relativity (col (4)) with the normalized current relativity (col (6)). It's only on page E-4 (loss ratio method) that they skip the credibility-weighting. In other words, they do their example in accordance with your 2nd paragraph. It makes sense not to normalize when using the loss ratio method because that method gives us an indication of the percentages by which the relativities need to be changed--we should not be converting the indications to relativities and then credibility-weighting those, which seems to be what you were thinking at first.

[TheZaha]

I dropped the ball on this a bit - thanks for the response.

You are right actuarialista, the methods are techinically equivalent.

However, I'm still not sure I 100% agree with how they are doing it. I guess it depends on what the complement of credibility is. Most problems say the complement is "no change" - does that mean no change to the relativities compared to the base or compared to the overall loss ratio. The answer would be different right?

Techincally the formula for the indicated relativity change (lets say using LR approach) is Loss Ratio for level i / loss ratio for level b. if there is no credibility, then yes dividing the numerator and denominator by all level loss ratio would yield the same result. However, when bringing in credibility, is it appropriate to calculate a change factor for relativity to total (weighted with no change) then rebase? Seems like there is a mismatch. The answers always come out close yet different.

so what i was saying was to credibility weight in change factors, but the change factors of the relativities compared to the base not to the total (i.e. don't normalize?).

[asile]

Is this the right explanation for why no normalizing on the LR approach?

Pure Premium approach - reviewing the loss cost at each level of the rating variable compared to the average yields an indicated relativity. We need to blend this with the existing relativity - we normalize the existing relativity for an apples vs apples comparison.

Loss ratio approach yields indicated change in relativity required to return each level of the rating variable to the average overall profitability. We credibility weight against no change (typically). You can't normalize the current ones before applying the change because you have no exposure to do so with. I guess maybe you could get a more accurate indicated "final" relativity if you had exposures by normalizing the current relativities before applying the cred wtd differentials?? Thoughts?

I really confused myself by working on the pre-2000 exam problems, the Finger-based solutions are not all that consistent with a WM approach. I think I am going to step back and really focus on the more recent/WM-based problems.