Old CAS 4B Credibility question

[BC]

I am trying to remember the credibility standard based on number of claims... it's something like

"If there are 1082 * (1 + Cv^2) Claims, then the expected loss ratio will be within 5% of the actual loss ratio 95% of the time..." or something.

Could someone please help me find the correct wording and generalization? My book is in another city.

Thanks

[PAC]

It sounds like you're referencing a limited fluctuation full credibility standard..."the number of observed claims required so the expected aggregate losses are within +/-c% of the true value (1-a)% of the time."

Assuming CLT and a poisson distribution for claim counts, the general formulas for full credibility are (using MS excel functions) ...

Frequency = (normsinv[ (1+(1-a))/2 ] /c )^2

Pure premiums = (1+CV^2) * (normsinv[ (1+(1-a))/2 ] / c )^2

e.g. using c=5.0%, a = 0.1, CV = 0.9

Frequency = ( normsinv[ (1+(1-.1))/2 ] / 0.05 )^2 = 1082

Pure premiums = (1+.9^2) * 1082 = 1958

[BC]

Yep, that's what I was looking for.

Thanks!