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 principle 1 but not principles 2,3, and 4.
• 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.)

So let's think through this...

The first principle looks like a definition. It's defining the term rate and mentions that it's based on future costs. That's why insurance ratemaking is prospective.

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

Alice doesn't quite understand the purpose of the second principle however. 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.

It doesn't seems possible for a rate to satisfy principle 3 but to not satisfy principle 2. That seems to imply that principle 2 is not necessary.