Even though each accident year's future emergence is estimated as a
factor times a single estimate of expected ultimate, the factors of
course differ by age. Thus by absorbing the expected ultimate into each
factor, you end up with an additive constant for each age, i.e.,
a(i)=f(i) x E(U). By differencing these you get additive constants for
each expected incremental emerged. Thus CC is like the usual link factor
method, but link sums are used instead of link factors. Thus sometines
CC is called the additive chain ladder.
Of course the additive links have to be estimated. Backing them out from
Stanard's estimates of future emerged is one of several ways of doing
this. I believe the best way to do it is to try to determine the
distribution of the actual emerged around the expected, and use MLE to
estimate the parameters. It could be argued that a least-squares
approach would give the minimum variance unbiased estimate without
specifying a distribution, but the problem with this is that minimum
variance estimates can give very unsatisfactory results (e.g., very high
percentage errors) when distributions are far from normal. As the MLE of
the normal is the least squares estimate, doing MLE after assuming
normal gives the least squares result. If you are uncomfortable about
assuming normal you should be equally uncomfortable about least squares.
Fortunately the distirbution of the emerged around the mean can be
tested with the triangulated data.
Gary G Venter
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