Part 5, Q.15

[Howard Mahler]

2004 Part 5, Question 15:

Which of the following increase for successively higher layers of loss?
1. Incremental increased limits factors.

I know statement #1 is false.
I can prove it.
I can find it in the literature.

My question is where is this on the Part 5 Syllabus.
(I checked Lange and elsewhere and could not find it.)

Thanks in advance,

Howard Mahler

[mathseal]

Howard,
I recall this being a central point in the Miccolis-Rosenberg paper (part 9).
But I'm suprised this statement is not in Lange (since he mentions that both development and trend seem to increase in higher layers).

Anyone find it?

[Mapie22]

Hi Howard,

I also tried looking for it, but was unable to find it. Sorry. One of my coworkers took and passed Exam 5 this spring. He's out of the office until tomorrow, but I'll ask him then if he remembers.

[Avi]

I do not remember it either (and I sat for this past exam). Lange only mentions that ILF's increase as the layer rises (bottom of page 167).

Lucky for me, on the exam itself, I knew that 2 was incorrect and that 3 was correct, and there was no answer 1 & 3 only. I put it off, completed the rest of the exam, and when I cam back to it, the word "incremental" finally struck me. While I cannot prove it, from the little work I've done, I have seen that ILF's seem to be concave downward, and thus increase at a decreasing rate which implies that although the incrementals remain positive, they decrease, and so the answer must have been B. But I did not recall anything from the syllabus.

[Howard Mahler]

The basic reason the incremental ILFs decrease is the same as the reason why the Coinsurance Premiums increase at a decreasing rate.
For a given width, lower layers of loss are larger than higher layers of loss.

As has been mentioned this is explicitly covered on Part 9.

I am getting suspicious that since the statement on the exam is false, and therefore clearly not stated by any of the authors on Part 5, you can answer not true, just as you can for many other not true statements.

It would be better if somewhere on the Part 5 syllabus we had the reverse of the false statement on the exam.
The incremental ILFs decrease.

Howard Mahler