September 2017 Question 6 (ii) - Exposure curves

I have a few questions on this question specifically - which hopefully should end my constant uphill battle with the exposure curve concept...

These are the column headings:
1st column: % of Maximum Probable Loss
2nd column: Total value of losses <= (x% of MPL)
3rd column: Total of x% of MPL , for all losses which are > x% of MPL

To derive the exposure curve, this involves summing up the values from the second and third columns of the table, which gives you your accumulated loss cost for the 1st x%, then dividing this by 25,000 which is the total loss <= 100% of the MPL. This gives you G(x) for each x%.

1) I'm having a bit of trouble interpreting both the second and third columns, particularly the third. Please correct me if I'm wrong - does the third column represent the losses that because are > x% of the MPL, have been limited to x% of the MPL, and then summed up? So referring to Chapter 15 Equation 1.2, in the second equality, the first expression refers to the second column and the second expression the third column.

2) Would it be safe to assume that for each loss, the MPL is the same? Or is the second column essentially combining all losses less than x% of their respective MPL? I don't think this would make sense given that the MPL should be a constant value in the case of exposure curves. I think the fact that this is a treaty reinsurance contracts adds credibility to the fact that the MPL is the same.

3) Why do we divide the accumulated loss cost for each x% by 25,000? Assuming the accumulated loss cost for each x% = LEV(x), does 25,000 = E[X] i.e. the expected total losses? What I'm failing to understand is why we aren't dividing LEV(x) by E[Y] i.e. the expected total losses as a proportion of the MPL. Is this because both LEV(x) and E[X] are expressed as the expected total losses, rather than being expressed as a ratio of the MPL?

Thanks in advance!

 

Let L be loss amount,
second column is \( \sum\limits_{L<=(x\%~of~MPL)} L \)

third column is\( \sum\limits_{L>(x\%~of~MPL)} (x\%~of~MPL) \)

you first interpretation is good, but the values do not add as Limited Expected value, sums are just limited.

I think there is no need to assume whether the MPL are same.
Main point to consider is "To what extent is the relative loss size distribution Y, and hence the exposure curve,
independent of the individual characteristics of the risk?" and relative homogeneity of data ... section 2.2 of chapter Rating using original loss curves explained in details.

so if the rowwise sum of column 2-3 are limited aggregation of amount, they can directly by divided by accumulated loss cost with limit of 100% of MPL, to get G(x).