07-25-2007, 09:46 AM
Can anyone tell me what is the intuition behind using the per occurance charge in the Loss Ratio method by Siewert?
07-25-2007, 09:47 AM
Also what does he mean by per aggregate charge?
Once again, the CAS, in its infinite wisdom, assigns a paper on Part 6 that presupposes knowledge studied (and agonized over) in part 9.
Deja Vu: http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?p=2212891#post2212891
For retrospectively-rated policies, there is a deposit premium that is paid up-front, and then the premium is adjusted, after the policy period is over, to reflect the actual losses that the insured had.
Those losses can be "capped" in two ways. The most common way is to say that the amount of loss that can be "recovered" from the insured is capped at an aggregate maximum; anything over that is paid out-of-pocket by the reinsurer. This is the "aggregate loss limit". It's the opposite, in a sense, from standard XOL pricing where an aggregate limit is the maximum the insured can submit to a treaty on a per-occurrence basis. This is because WC retro policies are written to cover ALL losses, and, are actually paid FIRST by the insurer and then recovered from the insured (see part 9 -- Teng).
Of course, there is no such thing as a free lunch, so the insured must "pay" for the fact that excess losses will not enter into the insurer's recovered losses. It does so by paying an "insurance charge", which (when offset by any "insurance savings" due to any minimum premium) will set the EXPECTED final retro premium equal to the expected PROSPECTIVE premium (Expected losses loaded for ALAE and expenses). That is the "aggregate charge."
How to calculate this is a very significant portion of Part 9 (Table M, Brosious, etc).
Another way for the insured to "smooth" their experience is to also cap EACH INDIVIDUAL loss that enters the retrospective premium adjustment. For example, the insured decided that it wants coverage, but at the end of the year, when it tallies up the losses it has to repay the insurer, it will cap each loss at 100K (and it may or may not have an aggrgate cap to boot). Once again, TINSTAAFL, so the insurer recovers the expected "excess" loss per occurrence over the occurrence cap as part of the basic premium, similar to the aggregate limit. This is the "per occurrence" charge. See Part 9, Table L and Brosius papers.
What Siewart is trying to do, if I remember correctly, is use the existing Table L and M data to calculate High Deductible excess WC. If you have a WC policy attaching at a high level, you are providing coverage for a high excess (potentially unlimited) layer. So, if you can figure out what entry ratio corresponds to the deductible, the "occurrence charge" at that entry ratio is directly related to the expected dollar amount of loss ABOVE that deductible for each loss occurrence! So P\cdot E \cdot \chi is the dollar amount, PER OCCURRENCE, of losses excess the deductible which corresponds to \chi.
Similarly, the aggregate charge is is the sum of the amount of each loss, UNDER THE OCCURRENCE CAP, that exceeds the aggregate cap (the stuff above the occurrence limit is handled by the occurrence charge). So P\cdot E\cdot\(1-\chi)\cdot\phi is the dollar amount of loss, below the occurrence cap, but over the aggregate cap, which the insurer will have to cover.
Summing all of the above, if I recall/understand now Siewart correctly, will give the expected dollar amounts of loss that this contract will cover. I believe Siewart wants to use this where there is little credible company experience, as a method of exposure rating.
I hope someone corrects me if I made a mistake, and good luck!
07-30-2007, 11:14 PM
Very helpful post(s), Avi (including the post in the link). These should be required readings for all taking Exam 9; I know I have a much better understanding of Table M after reading (and digesting) these two posts.
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