Attained Age Funding Method

I've just finished going through the funding methods and have a couple of initial questions.

1) The AAAL is defined as
i) Total fund required for benefits at retirement (or I suppose any other decrement) less value of contributions (SCR) to date;
which should be the same as
ii) value of accumulated past benefits.

The second way is the same as the Projected Unit AL and I think its the way used in practice (at least in my office).
However, while the 2 are identical for an individual, for a Plan they might not be. I think this is so (correct me if I'm wrong) and it occurs because the AASCR (for the Plan) is a weighted average (anyone know what the weights are eg Future service*salary) so the final sums are not quite the same.
Does this mean only one of the "definations" is correct and that only one way is correct to use?

2) The second question concerns Death in service Lump sums of x times saalry (and similar benefits). How are these to be treated eg as past accrued benefit(accrued/vested from day 1) or for future accrual.
If future accrual, then PU is fine you fund each future year like a Premium for 1 yr temp life. But what about AA? With AA you assume its going to accrue uniformly over the future service which is fine (like an n yr temp assurance), but what happens at the next valuation (say 3 years down the line)? Shouldnt some of the past contributions be set aside as a Past Service Liability for Death in Service?
I've even seen AA used for all but Death in service with a PU calculated death in service added on.

If you have any ideas/views/opinions about the above questions I would appreciate them, even without a full answer. I know I'm just picking at all the fine points and agree that they wouldnt make any material difference, but I would still like to understand the fundamental principles (which is what I prefer to do rather than learn all the answers).

 

It's been a while since I worked in pensions, so I may be rusty.

Here's my views.

1) For the scheme, the AASCR would be worked out as follows:

- work out NPV of (NRA - x_i) years of future service allowing for all decrements (assume each member is age x_i at the valn date). Call this future benefit value F_i

- work out NPV value of (NRA - x_i) years of future salary, call this S_i

Then AASCR = sum(F_i) / sum(S_i)

So if we say AAAL = Total NPV of benefits at retirement - val of future contributions and denote the past service reserve for individual i as P_i
then we have:

AAAL = sum(P_i) + sum(F_i) - AASCR x sum(S_i)
= sum(P_i) + sum(F_i) - sum(F_i) / sum(S_i)
x sum(S_i)
= sum(P_i)

which proves point 1 is true in the scheme sense as well as the individual.

2) The choice is up to the scheme actuary. Some do not reserve for DIS in the PSR others will reserve proportion N / NS in the past and (NS - N)/NS in the future. Also depends if scheme purchases life cover or not.

Hope this helps. Don't count on me being right here...it's been a long time!

 

Thanks Gareth

I should have spent more time thinking about it. That seems right to me.
My problem was that I was using the average rate on each individual and this gives slightly different AL's for individuals. I didnt realise that the total would be the same (less rounding errors and calculation mistakes). Also now that I think about it, it seems to be sensible to keep individual SCR with individual AL and Scheme SCR with Scheme AL and not try to mix the two.