Spring 2007 Exam, q.26

[allenlod]

The question is as follows:

"The following table was calculated based on loss amounts for a group of motorcycle insurance policies:

cj dj uj xj Pj
250 6 0 1 0
500 6 0 2 5
1000 7 1 4 9
2750 0 1 7 11
5500 0 1 1 3
6000 0 0 1 1
10,000 0 0 0 0

You are given α= 1 and β= 0.


Using the procedure in the Loss Models text, estimate the probability that a policy with a deductible of 500 will have a claim payment in excess of 5500."

The solution computed S(500) by taking the Kaplan-Meier estimate at the 250 deductible line but not including the 500 deductible line. I had 3 questions:

1. Why wasn't the information at the 500 line incorporated in calculating S(500)?
2. Is there a way to word the question differently so that the information at the 500 line would be included?
3. If I faced a similar situation with a Nelson-Aalen equivalent, would this still be the case?

Thanks in advance.

[Sophie H.]

1. given d=500 means data at 500 are truncated.
so, the $500 losses assumed to happen between 500 and 1000 and you include the $500 losses information in the next interval S(1000) (or S(2750)...,etc) .

i'll save the latter two questions for the next person :lol::lol:

[GooseyGoose]

2. Not really. You can make the deductible 499 or less.
3. Yes.

[allenlod]

Thanks to the both of you for the help :)

[Rushfan70]

I still can't see why S(500) isn't 5/6 * 9/11

[uclatommy]

I would tend to agree that the definition of S(500) is Pr(t>500) rather than Pr(t>=500) so it seems strange that they would not include the deaths at time 500 to calculate S(500). Anyone have insights?

[chopsuey]

what does the a = 1 b = 0 notation stand for?

[Clam Chowdah]

what does the a = 1 b = 0 notation stand for?

http://www.aceyourexams.net/errata/ExamCFall2009Changes.pdf

Also, the material on Approximations for Large Data Sets (Lesson 25) no longer uses \alpha, \beta, and Pj notation.

[chopsuey]

tyvm

[Rushfan70]

Digging into this, I found that, ironically, Stu liked this problem enough to put it exactly in the exercises of the new LM edition (14.35). I have the solutions manual, but it sheds no more light than Broverman.

Apparently large data sets with ranges (cj , cj+1), S(cj) stops at (cj-1 , cj). As the saying goes, with mathematics, you don't learn things, you just get used to them.