Out of curiosity what's the reasoning you couldn't just use the absolute value of X-50 to produce the desired result? X >= 0 by definition, right? What am I missing?
The way you say that, for all 0≤X 0. In English, this is saying that for a loss less than 50, the deductible of 50 requires some positive, non-zero amount that the insurance company must pay... this is wrong. It's probably easier to think about this in the context of what's actually going on. Let's say X = $40 represents the loss of a policyholder's car getting rear-ended. The deductible, d, of $50 means that the insurance company will not pay anything until the policyholder has paid greater than or equal to $50. If the policyholder pays the entire loss of $40, they have still paid less than $50, so the insurance company pays $0. This makes more sense than having the insurance company pay $10 (which is |40-50|), because the policyholder would have already paid the entire loss.
Is this material on SOA Exam P? How many questions do they usually have on this subject?
Out of curiosity what's the reasoning you couldn't just use the absolute value of X-50 to produce the desired result? X >= 0 by definition, right? What am I missing?
The way you say that, for all 0≤X 0. In English, this is saying that for a loss less than 50, the deductible of 50 requires some positive, non-zero amount that the insurance company must pay... this is wrong.
It's probably easier to think about this in the context of what's actually going on. Let's say X = $40 represents the loss of a policyholder's car getting rear-ended. The deductible, d, of $50 means that the insurance company will not pay anything until the policyholder has paid greater than or equal to $50. If the policyholder pays the entire loss of $40, they have still paid less than $50, so the insurance company pays $0. This makes more sense than having the insurance company pay $10 (which is |40-50|), because the policyholder would have already paid the entire loss.