Negative Reserves

[sadie1990]

In Chapter 20 it says that gross premium reserves may initially be negative for non-linked business "partly due to initial expenses and partly due to capitalising the expected future profit."

Can someone explain this? As gross premium reserves would be calculated as
PV Outgo + PV Exps - PV Income, how could this being negative be attributed to initial expenses??

Thanks

 

[morrisja]

The gross premium reserve will not contain initial expenses which have been allowed for in the premium calculation.

For a RP NL contract, as soon as the contract is sold the gross premium reserve will be:

EPV(Benefits) + EPV(Renewal Expenses) - EPV(Future Premiums)


1. If the reserve is calculated on the pricing basis then our reserve on day 1 would equal:

-(initial expenses + profit priced into contract)


2. If the reserve is calculated on a more lenient (realistic) basis then the reserve on day 1 would equal:

-(initial expenses + profit priced into contract + extra profit capitalised from the more lenient basis)


3. If the reserve is calculated on a more prudent basis then the reserve on day 1 would equal:

-(initial expenses + profit priced into contract - loss capitalised from more prudent basis)


So the first 2 would be negative and the 3rd could be positive or negative depending on the level of prudence in the reserving basis (which would increase the loss we capitalise on day 1).

1. is probably the easiest to understand. If the product was priced with zero profit margin, and we reserved for it on inception we would expect our PV of future premiums to exceed expenses and benefits by exactly the initial expenses.

I'm open to correction if anything is inaccurate.