In the calculation of item (8) in the table, for example in year 2: 3,295.40=0.99×0.95×6,800-3,100 I would have thought that when we subtract (t-1)_V that we should subtract the ACTUAL reserve calculated for the previous year i.e. 2,915.55=0.95×0.99×3,100 --- rather than the "per policy" reserve of 3,100. Why do we subtract the 3,100?
...similarly for the interest on reserve calculation. I do understand that when we get to the "profit signature" calc we multiply by the probability in force. So i guess that is why the change in reserves and interest on reserves are calculated on a "per policy" basis... However looking back at the "profit" cashflow in part (i) of the question how can item (10) profit be calculated on the "in force cashflows" combined with the "per policy" change in reserve and interest on reserve cashflows?
Answering your last point first, the phrase "in force cashflows" is short for "the cashflows expected per policy in force at the start of the year". So they are consistent with the increase in reserves, calculated on a per-policy-in-force-at-the-start-of-the-year basis. If you need convincing about the cashflow - you will see that the premium is included IN FULL in the "in force cashflow" for the year. So that's the amount of premium paid for a policy in force at the beginning of the year - it has not been multiplied by any in-force probability. As you say, that happens at the end, when we multiply the in-force PROFIT by the probability of an initial policy still being in force at the start of the relevant year. So I think, in your second post, you have answered your own question. The increase in reserve calculation is performed per policy in force at the start of the year, and so the start year reserve that applies is just the 3100. Good luck!
Thanks Robert I was getting confused! That helps clarify. Do everything on a per policy basis up to the profit vector, then to get your profit signature, multiply by probability of initial policy still being in force at the beginning of the year in order to actually be subject to those cashflows..
