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pirates
05-01-2002, 11:19 AM
Could someone please explain why you don't get the answer to this question if you use the formula in the ASM manual. Since they are asking for pure premium I used:

(y/k)^2*(Var(N)/E(N) + Var(X)/E(X)^2)

It only works if you calculate E(S) and V(S) and then just do

(y/k)^2 (Var(S)/E(S)^2)

why doesn't it work with the first formula - am I just losing it?

phdmom
05-01-2002, 12:05 PM
It's something to do with exposures vs. claims (I think?)

The formula you used, Var(N)/E[N] + Var(X)/E[X]^2, is the same as Var(S)/E[S]^2 divided by E[N].

(since when you add the fractions you get (E[X]^2*Var(N)+E[N]*Var(X))/E[N]*E[X]^2; the numerator is Var(S) and the denominator is E[S]^2/E[N]. )

I remember some sentence in the ASM about dividing by mean claim count if it asks for exposures (i.e. number of insureds), so that's why the second formula works. I think.

Someone else can probably explain it better.

MathGuy
05-01-2002, 12:06 PM
The problem is being asked in terms of exposures, not claims. The answer you get for the first formula is the number of claims needed for full credibility. Divide this by the expected frequency to get the exposures needed for full credibility.

We just discussed this on the CAS mailing list, as a matter of fact.

IOWA ACTUARY
05-01-2002, 02:12 PM
See posts from the 25th. I had same question. Has to do with exposures.