A per-occurrence deductible reduces the losses which count towards the aggregate deductible. If we price each piece separately without adjusting the expected losses used to price the aggregate deductible then we'll double count losses and so overprice.
Area W will be double counted unless we adjust to use F_D instead of F when pricing the aggregate deductible.
The ICRLL procedure recognizes that you get a flatter curve (more like F_D) when losses are more stable/less skewed. This happens when a risk has a greater volume of losses as this reduces volatility. The ICRLL adjustment produces an adjusted expected loss which is (typically) higher and so more stable. The more stable losses produce a lower insurance charge because there's less uncertainty about when it will exceed the aggregate deductible. (Higher expected losses correspond to lower expected loss groups. The lower the expected loss group, the smaller its insurance charge.)
Since the new insurance charge for the aggregate deductible is smaller, this means the overlap region W is smaller to non-existent and thus the ICRLL method produces a reasonably accurate insurance charge when both per-occurrence and aggregate deductibles are present.
Comments
A per-occurrence deductible reduces the losses which count towards the aggregate deductible. If we price each piece separately without adjusting the expected losses used to price the aggregate deductible then we'll double count losses and so overprice.
Look at the Lee diagram in
Area W will be double counted unless we adjust to use F_D instead of F when pricing the aggregate deductible.
The ICRLL procedure recognizes that you get a flatter curve (more like F_D) when losses are more stable/less skewed. This happens when a risk has a greater volume of losses as this reduces volatility. The ICRLL adjustment produces an adjusted expected loss which is (typically) higher and so more stable. The more stable losses produce a lower insurance charge because there's less uncertainty about when it will exceed the aggregate deductible. (Higher expected losses correspond to lower expected loss groups. The lower the expected loss group, the smaller its insurance charge.)
Since the new insurance charge for the aggregate deductible is smaller, this means the overlap region W is smaller to non-existent and thus the ICRLL method produces a reasonably accurate insurance charge when both per-occurrence and aggregate deductibles are present.