Oh! I think I get it now
So, for example,
If the insured is covered for 50,000 per month and he's 64:11 now then he can get
A: 50000 if he falls ill now
If he's 64:10 now then he can get
B: 100,000 (50,000 for 2 months till he is 65) if he falls ill before 64:11
or
C: 50,000 if he falls ill between 64:11 and 65 having survived till 64:11.
So, I factor in the probabilities of these events happening and then find the present values of these amounts.
Then, on the premium side of things:
If 64:10 today, then the insurer receives a premium (X) now, and again (X) at 64:11 with probability corresponding to survival AND not getting ill. This second X is discounted to today.
If 64:11 then we receive a premium (Y) now, equal to the present value of A above.
Now to test this, if I let (X) be equal to (Y), then the premium received now at age 64:10, i.e. (Y), will cover an amount not more than the present value of A.
And, the present value of C is less than the present value of A but it's probably quite close to the present value of A because the probability of surviving one month, even at age 64:10, is relatively high (at least according to the table I am using). Anyway, the PV of C seems to be covered by the first (Y) that we definitely receive.
However, the present value of B is obviously much greater than the present value of A though. So the second (Y) that we will probably receive and discounted to today would not cover that!
So (Y) is insufficient as a premium for someone aged 64:10 now, because it only just covers the expected cost due to C, but doesn't nearly cover the cost expected due to B.
So I think I'm seeing what's happening now...
And I seem to see that the turning point (where the premiums stop increasing with age and then start decreasing) is dependent on several assumptions made:
Interest rate used
Benefit amount chosen
Probabilities of survival and falling ill
Changing these can change the sensitivity of your results..
Am I reasoning this out correctly now? Or is there more to this puzzle?
Many thanks!
Last edited by a moderator: Jul 17, 2012