way to reduce initial capital strain under grass premium method

[uktous]

Hi,

When we calculate unit reserve for unit linked product, we can use actuarial funding.

When we calculate the reserve for a without profit product under gross premium method, how can we reduce to initial capital strain?
(Apart from redesign the product and weakening the basis.)

Thanks

 

[Robert Chadburn]

Hi
You can potentially reduce new business strain if there are items of future income that are being used to pay for initial expenses. So, in a unit-linked contract, if there are high future regular fund management charges for this purpose, then you can discount them and take them off your reserve value (using actuarial funding, like you say).

With a conventional contract, the "charges" to pay for the initial expenses are included in (ie are part of) the regular gross premium. We take off the present value of the future gross premiums in our reserve calculation, which will automatically include these future "charges". So, by performing a gross premium valuation, we have already reduced our new business strain by as much as we can, so there is no more that we can do.

Compare this with a net premium valuation (page 12 Chapter 20). Here we deduct the present value of the future net premiums only. But we are actually receiving more premiums than this in the future, which will include the loadings for initial expenses as above. So there is then scope for reducing new business strain by taking off the present value of these loadings in the reserve calculation (this is Zillmerisation).

As well as the things you mention, there are some other things you can do to reduce new business strain. Best one of these is some kind of financing reinsurance. (See section 1.3 of Chapter 26).

Hope this helps. Good luck

 

[Curious_actuary]

Hi

With a conventional contract, the "charges" to pay for the initial expenses are included in (ie are part of) the regular gross premium. We take off the present value of the future gross premiums in our reserve calculation, which will automatically include these future "charges". So, by performing a gross premium valuation, we have already reduced our new business strain by as much as we can, so there is no more that we can do.

Anybody please answer this, I have managed to confuse myself terribly with GPV and NB strain -

In case of the Gross premium Reserving, the reserves to hold are -

PV(benefits) + Initial expenses + PV(Renewal expenses) - PV(premiums)

At T=0
GPV = 0 (using premium basis and no profit assumption)

At T= 0+
GPV = First premium - Initial expenses - ---- 1)

We calculate the New Business strain as -

At T= 0+
NBS = Initial expenses + Reserves to hold - First premium

So from 1) and 2)

NBS = initial expenses + (First premium- initial expenses) - First premium = 0

So, in GPV (under premium basis) we do not face any new business strain??

However, if we take the prudent basis then the reserves at 0+ should be higher than (First premium - initial expenses) and we are likely to face new business strain.....

Thanks in advance

 

[Lynn Birchall]

Hi

I don't think you're as confused here as you think

What you've said in your post is correct.

We know that there are 2 causes of new business strain:
(1) Big initial expenses at time 0 being recouped out of items of future income
(2) Prudence of the statutoy reserving basis (and and solvency margin requirements).

For the GPV, we don't get new business strain as a result of (1) (because the method takes into account the value of the future premium income that is recouping the initial expenses).

As you said, we will however get new business strain as a result of (2).

 

[Curious_actuary]

Thanks for the reply Lynn.