• There may be enough data to update the per-occurrence excess charge most often than the aggregate excess charge.

I don't understand what this means. Should it be more often instead of most often? Even then, what's the reason that we'd like to update the per-occurrence limit more often than the aggregate limit? Is it because that's the limit getting hit more often?

In this question, there is a single loss of 150K.

The ratable loss is 100K (due to the incident limit of 100K).

The 50K in excess of the incident limit are already priced for through the excess loss premium.

Therefore, (and this is the question... more of a confirmation than a question): the insurer does pay the full 150K claim, but only adjusts the premium based on the ratable loss. I.e. the insured pays a difference in premium, but does not retain any part of the loss.

Correct?

Limited Table M, on the other hand, expresses the aggregate insurance charge on the basis of limited expected losses in the denominator, and then (like Table L) adds the per-occurrence charge k, which is proportional to unlimited expected losses (E). Because of this basis difference, we cannot add the two ratios and store them together in one table since they must each be applied to a different claim exposure base. I think this is why we call it a 2-step method even though Table L also must derive k as a second step then add it to the aggregate charge estimate.

To help verify my understanding of the linkage between the two methods, I tried estimating the Limited Table M insurance charge estimate for Source text: Chapter 3 Q14. Compared to the Table L estimate we get r_D = 1.5 x 250/200 = 1.875, and then integrating with a Uniform(0,2) limited entry ratio distribution (instead of U(0,1.6) for Table L), we get phi_D(1.875) = 1.25 x (phi*(1.5)-k) = E/E_D * (phi(1.5) - k), exactly the basis the change I was expecting. This then shows that both methods add the value of k on-top of this aggregate charge estimate, except that Limited Table M cannot add the 2 ratios together to store in a common table due to the basis difference.

So this is where my question begins. Table L overcame the basis difference between the aggregate and per-occurrence charge by expressing the aggregate charge on the basis of E to match k. Is there good reason why Limited Table M could not have alternatively re-expressed k on the basis of limited expected losses to match the base of its aggregate insurance charge? Then the 2 could be summed, and in theory applied to an estimate of limited expected losses instead of vs. unlimited claims like for Table L.

I'm trying to reason why this is not a considered alternative; I don't think I've seen justification for this in the reading, but this seems like an interesting comparison to draw. Would the problem with this latter alternative be that excess per-occurrence claims relative to limited claims would not normalize for policy size or severity skewness as well, and thus contain too much over-dispersion to yield reliable estimates? I'm not totally certain on this reasoning yet, just trying to think my way through it now so I won't have to on the exam if needed. Curious to hear what others' thoughts are, or if I've maybe gone astray while thinking my way through any of the above details.

Thanks!