From: firstname.lastname@example.org <email@example.com>
To: firstname.lastname@example.org <email@example.com>
Date: Friday, May 07, 1999 1:56 PM
Subject: Credibility Experts?
>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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