What I think is that when you calculate AS, you do it for an average policy but would need to scale it up to reflect the actual in-force business at end of each valuation year (say).
So, for a product that has just been sold:
1. The first set of premiums say from 1000 PH's are collected, then take off the expenses incurred relating to the contracts. The remaining premiums are invested in some selected mix of assets.
2. These premiums then earn an investment return so that the AS before any deductions is AS_bef (say)
3. Now suppose, at the end of the year, mortality 1%, then there are 10 PH who die. Their death benefits will be paid. Death benefit paid = 10*death benefit OR can also be written as 1%*1000*death benefit
4. There will be some who withdraw and depending if there are withdrawals allowed & any guaranteed positive surrender value, this will have to be allowed too.
5. Then AS_aft = AS_bef - 3 - 4
6. Then the remaining AS is for those PH who are alive at the end of the term.
i.e. AS per policy = AS_bef/ 990
OR AS per policy = AS-bef/ {1000 - 1%*1000}
Now if you do the same calcs from 1 to 6, but replace the 1000 PH's with only 1 PH you will see the mortality costs on average per PH and also notice that the AS is spread between the remaining PH who are alive and so we divide by px.
Also, I think that the death charge being subtracted from the fund of a living PH is actually a charge from total AS before any deaths, i.e. we first calculate the AS for all PH and then take off the mortality charge. I also think it has to do with the pooling of risks concept that insurance is based on.
Hope this helps, but would suggest you wait for a few more replies, just to confirm.
