confusion on Modifying Frequency (ASM supp 12 & 13)

[IcyBear]

could anyone please help me? I'm really sorry if this has been asked before but I did a quick search on this forum and nothing came up.

I'm a little confused on when deductibles affect frequency and when it doesn't. I understand from the example on page 165 of ASM supplement that when a deductible is introduced, N (the frequency var.) is modified by the probability of a claim > 0; while X (the severity var.) is E[(X-d)+].

However, question 12.7(SOA3-F04:17): E[aggregated payment] = E[(X-d)+]*E[N] where N~Possion(lambda=5) and lambda is NOT modified by 5*(1-F[d])

question 13.47(CAS3-S04:19): again the deductible only affects severity and not frequency.

Sorry for the long post, but is my understanding correct that when a deductible is introduced, both X & N variables should be modified?

Thank you! Any help would be greatly appreciated!

[Gandalf]

You might have some luck searching in MLC, since this material used to be on M. (The forum now called MLC was for all of the old M).

If you modify the frequency to correspond to cases in excess of the deductible, then you must modify the severity to be the conditional distribution, given that the loss exceeds the deductible.

In the specific case of expected values, if you modify the frequency, then you need E{[(X-d)+]|X>d}. If you do not modify the frequency, then you need E[(X-d)+].

[Abraham Weishaus]

There are always 2 ways to do the problem, as Gandalf says. If you wish, redo the manual problems the other way and confirm that you get the same answer.