Hi the variance for the compound distributions of pure premium and loss ratios is claimed to be the same as the aggregate losses L=X1+X2+....XN however, both pure premiums and loss ratios have a denominator, (exposures and earned premiums) which when included inside the variance (i.e. Var(PP|N) should be taken outside of the bracket and this becomes (1/exposures)^2 *N*var(X) right? Same is true for E[PP|N] Or am I missing something?
Hi I agree with you that the variance of the aggregate losses is not the same as that of the pure premium as defined at the start of Section 2.4 (or that of the loss ratio). There is certainly something odd happening in the Core Reading. The number of claims N seems to be being used interchangeably with frequency in some places. I’ll draw this to the attention of the Profession. Many thanks Duncan
