Marker/Mohl, calculating earned exposures for a claims-made policy

[ftty]

I couldn't understand Example 3 in p.282 of the paper by Marker/Mohl.

The example is asking for the earned exposures of a mature claims-made policy written 1/3 of the way through year j. According to the errata, this policy contributes:
8/9 exposure to E[0,j]
1/9 exposure to E[0,j+1]

Would anyone please explain how this is calculated? Thanks.

[jk]

:confused: But they don't say that. They say it's 2/3 of an exposure for j and 1/3 for j+1, just like you would expect.

[ftty]

Who are "they"?

I was referring to the errata provided by CAS at:
http://www.casact.org/pubs/dpp/dpp80/errata.pdf

The summary I read in All10 also used the answers 8/9 and 1/9, but it didn't provide details about how they're calculated.

I suppose it has something to do with the "uniform earning" mentioned in the immediate paragraph, but just couldn't figure out how it works.

[jk]

I was reading the original article, not the errata. Now that I think about the numbers given in the errata, they do make sense, although it's almost impossible to explain without diagrams.

A full exposure to a year with lag 0 is a triangle. A full exposure to a year with any greater lag is a parallelogram. The exposure behind the mature claims-made policy is a vertical column, capturing claims occuring between May 1 of Year J and May 1 of J+1 with any lag. This column covers 8/9 of the (0,j) triangle, 1/9 of the (0,j+1) triangle, 2/3 of the rest of the Year J parallelograms, and 1/3 of the rest of the Year J+1 parallelograms.

It's confusing because the "algebraic lag" isn't equal to the "integer lag". In other words, if a claim occurs on September 1, 2004, and is reported on March 1, 2005, it's considered to have "lag 1". But the "algebraic lag" is only 0.5 years. The claim would be graphed in the upper left hand corner of the "Year 2005, lag 1" parallelogram. Apparently it even confused Marker & Mohl.