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Old 06-03-2020, 01:14 AM
Oceantrico Oceantrico is offline
Join Date: Apr 2020
Posts: 5
Default Bahnemann - Problem 6.6

TL : DR I have no idea how to prove this, any help will be appreciated.

Hi all, I am going through Bahnemann very slowly, my strategy is to try to work on related end-of-chapter problems as I finish a section of the chapter.

So I have just finished reading Section 6.2 and thought I would try out Problem 6.6. Embarrassed to say, this question is above my pay grade

To start off, my solutions are:
  • When l <= c, E[X ; l/(1+r)] * (1+r)
  • When l > c, E[X ; l - rc] + r * E[X ; c]
Obviously, these are different from the official solutions and this is kind of expected as I am not very good with stats.

Anyway I thought I should at least plug in some numbers to verify the official solutions which may help with my understanding and therefore proceeded to creating the spreadsheet attached.

Approach of the spreadsheet (sorry for the poor presentation):
  • Column labeled "X" - Generate some unlimited claim-size (indemnity-only) numbers. Here I chose to generate 20 claims.
  • Column labeled "Y" - Determine Y depending on an arbitrary choice of r and c.
  • Column labeled "Y;l" - Limit Y to an arbitrary choice of l (if applicable).
  • Cell D30 - Average value of cells under column labeled "Y;l" and I suppose this is what the question is asking for.
Out of my expectations, however, the official solutions do not seem to produce the right figures for me.

In particular, Cell E32 and G33 contain my calculations of the official solutions but (depending on the value of l and c) they do not match the value in Cell D30.

Incidentally, I also calculated the values using my solutions in Cell F35 and H36 which somehow seem to match the value in Cell D30 perfectly (When l is set to be <= c, Cell F35 matches Cell D30; when l is set to be > c, Cell H36 matches Cell D30).

Despite the above, it is not my intention to prove that the official solutions are wrong, especially since this question does not fall under Errata and also Bahnemann is indeed above my pay grade!

The question is though, where am I fundamentally wrong
Attached Files
File Type: xlsx P6.6.xlsx (13.1 KB, 19 views)
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Old 06-03-2020, 08:51 AM
sticks1839 sticks1839 is offline
Join Date: Jul 2005
Posts: 1,694

Looks to me like it's inconsistent application of the policy limit in regards to the ALAE. In your Y;l column, the limit l applies to the claim X plus the ALAE; but the solutions given for Problem 6.6 assume that the limit l applies only to loss portion X. This is evident because when the limit l applies to loss and ALAE, the r value should be set to 0 (reread page 166).

I admit that this is not 100% clear in the problem.
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Old 06-04-2020, 11:20 PM
Oceantrico Oceantrico is offline
Join Date: Apr 2020
Posts: 5

Many thanks, I surely need to reread the text!
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