Credibility Experts?

( john.t.devereux@us.pwcglobal.com )
Fri, 07 May 1999 13:53:49 -0500

I was recently posed a credibility question that, given my current level of
familiarity in the area, I've opted to post here for any potential comments
and suggested responses. A life actuary acquaintance of mine who performs
credit related work was reviewing the Credibility chapter (7) of the
Foundations of Casualty Actuarial Science book. He was reviewing formula
4.17A and formula 4.17B shown below:

Z(subscript: 1) = 1 / [ 1 + K ] and
Z(subscript: i+1) = 1 / [ 1 + 1 / (J + Z(subscript: i)) ]

Basically, his understanding was, that as J --> 0, (J being defined as d/v
or the change in variance over the variance) (i.e. minimizing the
fluctuation), the above formulas should revert to the familiar Z(subscript:
n) = n / [ n + K ]. The formulas actually simplify to Z(subscript: n) = 1
/ [ n + K ] when J=0. What are we missing? Is there a gap in his logic?
Is there no foundation for his assumption of n/[n+K]?

If there is someone out there who can offer their wisdom, I would rather
not (re)read the entire chapter and its references to brush up on my
credibility theory. Thanks
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