Fall 2015 #18
In Sample answer 2 for this question, I don't understand why a Table M is being built instead of a Table L where phi(2.0) is k=0.5?
In Sample answer 2 for this question, I don't understand why a Table M is being built instead of a Table L where phi(2.0) is k=0.5?
Comments
This question can definitely be solved using the Table L method. It's likely the CAS expected most candidates to take the "easier" route of pricing the per-occurrence and aggregate deductibles separately though.
When using the Table L method you need the unlimited loss as well as the loss limited by the per-occurrence deductible. From there you can calculate k=0.256 and build the Table L.
Lastly, the entry ratio you'll need to solve the problem is 450/403 = annual agg deductible / expected unlimited loss.
Thank you for clarifying!
This makes sense.
For the sample solution 1 I do not understand how they calculate the Excess of Aggregate Deductible. Given an occurrence deductible of 150,000 and aggregate deductible of 450,000. Specifically for Risk 4.
Ex:
Risk 4 has 4 claims at or above 150,000 so the total deductible losses limited is 600,000. The losses above 600,000 do not add up to 450,000 so I thought there was no excess losses but this is not the case, why is this?
The key here is understanding the relationship between the per-occurrence deductible and the aggregate deductible. Losses in excess of the per-occurrence deductible are used to price the per-occurrence deductible. Losses below the per-occurrence deductible have the aggregate deductible applied. Any amount in excess of the aggregate deductible is used to price the aggregate deductible.
Specifically, for risk 4. Each claim has a per-occurrence deductible of 150,000. Without the aggregate deductible, the insured would be responsible for 4x 150,000 = 600,000 and the insurer would pay the extra 150k + 250k + 200k + 150k - 600k = 150k. This 150k is used to price the per-occurrence deductible.
However, we also have an aggregate deductible of 450,000. This means the maximum out of pocket for the insured is 450k. So the 600k of per-occurrence deductible losses is capped at 450k by the aggregate deductible. The 600k - 450k = 150k (excess of the aggregate deductible) is used to price the aggregate deductible.
Overall, the insured for risk 4 is responsible for 450k of losses while the insurer is responsible for 150k (excess of per-occurrence) + 150k (excess of aggregate) = 300k.