Q1: in GPR features why it is said that difference between pricing and valuation basis will be immediately taken as profit or loss? Q2:Why reserve will be -be initially partly due to high initial expenses and due to prudence...since initial exp will be added in PV exp + PV benefit -PV prem ,how it will be -ve due to initial exp? Why prudence will make reserves -be , since prudence will also increase PV exp and benefits term? Q3: why GPR ignores future withdrawals since in basis we always consider basis of withdrawals also ? Q4: Relationship between pricing and reserving is quite confusing in chapter1 and in chapter 18 mentioned that pricing considers reserving setting cost ...plz explain.
I will answer each of your questions in turn below. Q1: in GPR features why it is said that difference between pricing and valuation basis will be immediately taken as profit or loss? Let's say we price using an equation of value as follows: EPV(all premiums) = EPV(all claims plus all expenses) on pricing basis The gross premium reserve at outset (just before the first premium is paid) is given by: GPR = EPV(all claims plus all expenses) - EPV(all premiums) on valuation basis If the valuation and pricing bases were the same then we would have a reserve of zero at outset, ie the premiums would be exactly enough to cover the claims and expenses. However, normally valuation and pricing bases are different. For example, we may set reserves assuming worse experience than was used to set premiums. Then on the reserving basis the premiums would be insufficient to cover claims and expenses and we would immediately have to set up a reserve to cover the difference. Q2:Why reserve will be -be initially partly due to high initial expenses and due to prudence...since initial exp will be added in PV exp + PV benefit -PV prem ,how it will be -ve due to initial exp? Why prudence will make reserves -be , since prudence will also increase PV exp and benefits term? We could price using an equation of value as follows: EPV(all premiums) = EPV(all claims plus all expenses) Separating out the first cashflow from the later cashflows we get: First premium + EPV(later premiums) = EPV(claims plus later expenses) + initial expense The gross premium reserve at outset (just after the first premium is paid) is given by: GPR = EPV(claims plus later expenses) - EPV(later premiums) Substituting in from the pricing equation (assuming the pricing and reserving bases are the same for simplicity) we get: GPR = First premium - initial expense The initial expenses are often very high compared to the first premium and so we get a negative reserve. The impact of prudence relates back to the answer to part (i). Q3: why GPR ignores future withdrawals since in basis we always consider basis of withdrawals also ? If we calculate the GPR using the formula approach then we will value the benefits using the big A function and the premiums / expenses using the little a function from the actuarial tables. These tables have been calculated allowing for mortality, but they make no allowance for withdrawals. Alternatively, we could calculate the GPR using a cashflow projection approach. We could allow for withdrawals in this method. Q4: Relationship between pricing and reserving is quite confusing in chapter1 and in chapter 18 mentioned that pricing considers reserving setting cost. If we calculate premiums using an equation of value, then we do not allow for reserves anywhere in the formula. However, in practice we would usually use a profit test to calculate premiums. Profit in year = Premiums - claims - expenses + interest on reserves - increase in reserves. So in this way we can allow for cost of setting up reserves. Best wishes Mark
Thanks for reply Mark! But still I am in a confusion regarding why reserve -ve(ignore initial expense ) due to prudence in reserve basis since by prudence in reserve basis I am increasing EPV of benefits and exp more than EPV premium (pricing basis) in GPR formula..mathematically it will lead to +ve reserves. IE EPV (benefit+exp) due to prudence are higher than premium pv ? Q2Similary how we are saying that keeping reserve prudent than premium basis ,we are capitalizing futureprofits( if experience turn out same as reserve basis ie worse than premium then we capitalized future losses not profit)?
Yes, you are correct that any prudence in the reserving basis would push reserves up. The notes don't say that prudence would make them negative, in Section 2.4 we say "reserves may initially be negative for non-linked business, partly due to initial expenses and partly due to capitalising the expected future profit". However, "any differences between the pricing and valuation bases will immediately be taken as profit or loss." So yes you are right, if the reserving basis is stronger (weaker) than the pricing basis we get a loss (profit). So when we "capitalise the expected profit", this profit may well be negative, ie a loss. There are two things to consider here. The premiums might be profitable because we have used a prudent pricing basis and / or because of an explicit profit margin. So there are two sources of profit to capitalise. Under the Solvency II regulations in the UK (and elsewhere in the EU) we use best estimate reserving assumptions, so both the prudence in the pricing basis and the profit loading are released immediately as profit under the GPR and we have negative reserves on many regular premium policies. The notes used to describe the net premium valuation approach, which in contrast, would have released these profits gradually each year. On the other hand, in jurisdictions where the reserving basis is prudent, we'd normally expect the reserving basis to be a lot more prudent than the pricing basis leading to an initial loss as you suggest. Best wishes Mark
