1. The reporting pattern for losses as a percent of ultimate is not a
probability distribution, since the cumulative reported percentage can exceed
100% at ages prior to ultimate.
2. Consider a steady state situation for AY losses. That is, an equal volume
of exposures having the same loss reporting pattern has been written uniformly
in all past years. Assuming that there's no seasonality to the losses, then
the reported losses (for all AY's combined) in any given calendar quarter
should be approximately constant. This implies that the emergence of losses
at ages 1, 2, 3, and 4 quarters of development for an accident year can be
determined if the emergence of losses at greater ages is known.
For example, suppose that the AY losses reach ultimate at 8 quarters of
development, and that the emergence in qtrs 5 through 8 is known. Let these
be 20% of the AY ultimate in qtr 5, 15% in qtr 6 , 12% in qtr 7, and 6% in qtr
8. Then the loss emergence in qtrs 1 through 4 as a percent of ultimate must
be 5%, 10%, 13%, and 19% of the AY ultimate, respectively.
So, if you have a reasonable estimate at the later ages, then you have a
reasonable estimate for the earlier ages as well. You can then decompose
these into Acc Qtr reporting patterns. In this example, this is 5, 5, 3, 6,
6, 0, 0, 0.
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