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Foundations of Casualty Actuarial Science
We can solve for the optimal credibility using least
squares regression. That is, by minimizing the sum of
squares (yi - yi). If we have data for N insured and
they all have the same credibility, the least squares
credibility formula will be :
Z = [ (i- 1) (yi - 1)] / N
[ (i - 1)2] /N
Where summations are over i, the individual insured.
The input data for these costs are relative in two different
time periods. Although we used claim count data, the
formula can work equally for claim amounts, at least
theoretically. In practice, individual insured experience
greatly increase the CV of the individual insured
experience .There will be much more sampling error if
we use amounts rather than counts.
d) Structure variance - Two other formulas are significant.
The first can be developed from the regression formula
and the general credibility formula.
2 = Z (2 + 2)
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