In analyzing premium rate changes on renewal, it says the main disadvantage of the method is that it ignores the impact of new and lost business written at different rates. What do they mean by lost business written at different rates? Is the reference to policies that dont renew? If they are written at different rates dont they need to be analyzed separately in the first place? Would you please explain what the core reading is saying?
The rate change measure is (total written premium at time 2)/(total written premium at time 1) -1. The point is that the numerator and the denominator aren't consistent: The numerator includes business that was written at time 2 but that wasn't written at time 1. Similarly the denominator includes business that was written at time at time 1 but not renewed at time 2. The phrase "written at different rates" rather clouds the issue in my view. The Core Reading is only saying you can't tell what the rate change is for these policies (eg we don't know what the premium was at time 1 for new business, and we don't know what the premium rate is at time 2 for lapsed business).
