Excess loss pure premium factor. It's notation from a paper that is no longer on the syllabus because the Fisher paper condensed several old papers into one text.
The ELPPF multiplied by the expected unlimited loss gives you the expected excess loss.
In this question, you'll use the ELPPF to price the excess of the per-occurrence deductible and then the insurance charge to price the excess of the aggregate deductible.
In our opinion, this exam question is ambiguous because it doesn't tell you what type of table of insurance charges you're given. Is it a limited table M or a regular table M?
The sample 1 solution assumes it is a regular table M and we're using that as an approximation to the limited table M. Since a regular table M uses E[A] rather than E[A_D] we multiply by the aggregate losses instead of the limited losses.
The sample 2 solution assumes it's a limited table M so we multiply by E[A_D] = E[A]*(1-ELPFF) = 900,000 * 0.8
Comments
Excess loss pure premium factor. It's notation from a paper that is no longer on the syllabus because the Fisher paper condensed several old papers into one text.
The ELPPF multiplied by the expected unlimited loss gives you the expected excess loss.
In this question, you'll use the ELPPF to price the excess of the per-occurrence deductible and then the insurance charge to price the excess of the aggregate deductible.
Why is the insurance charge being multiplied by the aggregate losses instead of the limited losses to get the aggregate excess loss cost?
In our opinion, this exam question is ambiguous because it doesn't tell you what type of table of insurance charges you're given. Is it a limited table M or a regular table M?
The sample 1 solution assumes it is a regular table M and we're using that as an approximation to the limited table M. Since a regular table M uses E[A] rather than E[A_D] we multiply by the aggregate losses instead of the limited losses.
The sample 2 solution assumes it's a limited table M so we multiply by E[A_D] = E[A]*(1-ELPFF) = 900,000 * 0.8