Supervisory Reserves (2)

[Avviey]

I have 3 questions here:

1) Q21.5 on page 6, I understand that if a policy surrenders in the future and a profit will be made equal to the excess of the supervisory reserve at that time over the surrender valuse paid at that time. But I dont understand why this normally mean that the current supervisory reserve allowing for future surrenders will be less than one that assumes no future surrenders. I would think the other way around, ie. more ?

2) "Where no explicit allowance is made for future bonuses, a rate of interest used should be lower than the rate chosen by an apporpriate amount." This is the one of the reseving principle on page 6 as well, I wonder the rationale behind this, as I dont follow the example given on that page.

3) When we say "ZNP include implicit allowance for future bonuses and expenses for any current inforce policies" I know the implicit allowance for expenses which is the Zillmer adjustment, but Zillmer adjustment will also include future bonus part?

Heaps of thanks.

 

[fischer]

1) I'm only attempting the 1st ques now.
Without allowing for withdrawals
Res at end =

{(Res at start + premiums - expenses).(1+i) -(SA + claim expenses).q}/ p

Allowing for withdrawals
Res at end =

{(Res at start + premiums - expenses).(1+i) -(SA + claim expenses).q - (Surr_ben).w}/ p

So, mathematically we can see that allowing for withdrawals we have a lower reserve required.

Intuitively, we can say that if there were no withdrawals, then all policies (that don't die) would go to maturity. So, the company would need a large lumpsum in the end to pay all those policies maturing and so would need a larger reserve.

By allowing for withdrawals, the company will not have many maturities and so require a lower reserve.

 

[fischer]

2) Attempting the 2nd ques also!!
I have not looked at the example as yet, but the rationale behind using a lower interest rate if no explicit allowance is made for future bonuses is that the reserves calculated using the lower interest rate will be higher (than if calculated using the "standard" (i.e. valuation) interest rate) and so should be able to cover future bonuses alongwith guaranteed sum assured.
Looking at the formula in 1)
Res at end =

{(Res at start + premiums - expenses).(1+i) -(SA.(1+b) + claim expenses).q}/ p

I have explicitly allowed for future bonus here. So, the discount rate used to discount Res at end will be the valuation interest rate.
If the allowance for future bonus was not there, then a lower interest rate would be used so that the reserve calculated would be approximately same as if an explicit allowance for future bonuses was made.

 

[Avviey]

Thank you very very much, Fischer.
Only the 3rd question remains now.

Cheers.