Can anyone explain how the incidence of risk works in the solution to X4.12? The solution says 'Over the policy year, if the risk increases from 0 to say 2 units per day, then the total risk over the year is 1 unit'. I don't get this statement! How can the total risk over the year be 1 unit if the risk increases by 2 units per day? If someone can explain, for example, how the total risk units earned at the end of 2006 for business written in q1 2006 = 49/64, then I should be able to figure out how the q2, q3, and q4 calcs work.
I think it's the 'per day' comment that's a little confusing (as the risk is already per day). So let's ignore that for now. You can work in different "units of risk" if you like, as the units all cancel each other out anyway at the end. For the business written in the first quarter, 7/8 will be earned by the end of the year. And the risk is going up uniformly over the year, so by the time it gets 7/8 of the way through, the risk is 7/8 of its maximum. So the earned portion is 7/8 squared. Does this make it any easier to understand?
