Alice's Comment on the Ratemaking SOP

When Alice first learned about these 4 principles, she tried to think up concrete examples to help her understanding. Here's her reasoning:

• If these 4 principles are independent of each other, you should be able to invent an example of a rate that satisfies any three chosen principles but not the fourth.
• If these 4 principles are not independent of each other, then you don't need all 4. (This is like Euclid's axioms of geometry. The axioms represent the minimum number of assumptions required to be able to prove all the other theorems of geometry.)

Alice thought for a while but had trouble thinking up concrete examples. Let's think through this...

The first principle looks more like a definition than a principle and that's Alice's first point of confusion. It's defining the term prospective rate as one that's based on future costs.

Principle 1: A rate is an estimate of the expected value of future costs.

Alice now doesn't quite understand the purpose of the second principle. It seems to say the same thing as the first principle, just in slightly different words. In this context, future costs seems to be exactly the same thing as all costs associated with the transfer of risk.

Principle 2: A rate provides for all costs associated with the transfer of risk.

Then the third principle seems to imply the second principle. If the rate provides for all costs associated with individual risk transfer, then it automatically provides for all costs associated with aggregate risk transfer which is exactly what the second principle says.

Principle 3: A rate provides for the costs associated with an individual risk transfer.

(If it isn't possible for a rate to satisfy principle 3 but to not satisfy principle 2 then is principle 2 even necessary?)

Then principle 4 is simply defining the term actuarially sound. It seems to be putting a cap on rates whereas principles 2 & 3 are putting a floor on rates by requiring that all costs are covered.

Principle 4: A rate is reasonable and not excessive, inadequate, or unfairly discriminatory if it is an actuarially sound estimate of the expected value of all future costs associated with an individual risk transfer.

And what can you even say about the term unfairly discriminatory. That's a loaded term if there ever was one! Obviously you can't discriminate on the basis of race but you are permitted to discriminate on the basis of age and gender. Is that fair? Some women's groups are pushing for the gender distinction in auto rates to be eliminated even though that would make women's rates higher (and men's rates lower.)

All of this made Alice's head hurt more than a hangover the blowout party at the CAS annual meeting. Here's what she eventually came up with as a simple way to understand these ratemaking principles:

Alice's Principles: Use your highly-trained actuarial brain to accurately predict future costs. Build in a reasonable profit. Don't overcharge you customers.

Like I said, this extra discussion isn't part of the syllabus but Alice wanted me to include it as food for thought. Remember that for the exam you have to memorize these 4 principles and then have some general sense for they really mean.