Q8
When I first saw this problem, I was expecting to do Premium at basic*(ILF(1M) - C(500k)) where C(..) represent the loss elimination ratio. Why is it okay to use ILF(500k)?
Thanks!
When I first saw this problem, I was expecting to do Premium at basic*(ILF(1M) - C(500k)) where C(..) represent the loss elimination ratio. Why is it okay to use ILF(500k)?
Thanks!
Comments
An ILF for a limit L relative to a base limit b is calculated as E[X; L] / E[X; b]. A 500k limit over a 500k deductible corresponds to the layer of loss between 500k and 1m. So we need the expected loss limited to 1m less the expected loss limited to 500k. However, we're given the expected severities rather than the expected limited losses. We can see this because the expected basic limit severity is 58,750 while the expected basic limit indemnity is 65,000, i.e. there's a basic limit claim frequency of 1.106 implied.
If we divide E[X; 1m] - E[X; 500k] by E[X; b] then this is the difference of the ILFs at 1m and 500k. We can then use the basic limit premium (which reflects the frequency component) to get the premium for the layer.
This is the same as thinking (E[X; 1m] - E[X;500k]) * (65,000/E[X;b]) where the second multiplicative factor is the frequency adjustment.