the numbers given in the published solution under the column "indicated
relativities" of terr 1,2,3 as .967,1.813,.604 are what FINGER on page
268 column 12 in the finger exhibit in foundations of cas would refer
to as "preliminary adjustments". Preliminary adjustments of course for
the base class do not have to be 1.00, because the base territory can
be adjusted, even though its revised relativity still must be 1.0.
now because we are not given credibility to apply the finger
credibility complement of 1.0 for preliminary adjustments we have
credible adjustments of .967,1.813,.604 (assume fully credible) column
14 in finger exhibit on page 268. then finger page 268 column 15 gets
the extensions as the credible adjustments times the on level earned
premium so credible extensions would be
125000*.967+250000*1.813+300000*.604=755325;
this is assuming that the original on level earned premiums are the
correct premiums to balance to (not sure about this although dont know
what would happen if terr 1 on level earned premiums were used for off
balance calculation)
so the off balance factor now would seem to be 725000/755325= .9598
---- how confusing.
now column 16 page 268 finger balanced adjustments for each terr would
seem to be (the adjustment factor*credible adjustment) for each
territory so we have column 16 values for each terr as
..958*.967=.9264 for terr 1; .958*1.813=1.74 for second terr; and
..958*.604=.579 for third territory.
finally revised relativities would be for each territory
current territory rel*(bal adj for terr/base terr bal adj)
so for terr 1 revised rel is 1.0(.9264/.9264)=1.0
for terr 2 revised rel is 1.25*(1.74/.9264) =2.34777
and finally for terr 3 revised rel is .75*(.579/.9264)=.46875
everyone confused now? I am.
billg
billg5@yahoo.com
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