By strengthening the reserving basis, results in the PVIF being increased. (This was part of the the solution in 23.2). I also understand the profit formula is : Income minus Outgo minus change in Reserve So, is the reason for PVIF increasing, due to the reserving basis being strengthened, because of more reserves being released in the future. Thereby the "change in reserve" part of the equation above is negative and thus (with the double minus) - a positive impact on the profit ? What happens though with products that have reserves increasing over time (like an endowment)? The reserves here are building up and not reducing as time passes and thereby contributing a negative to the profit formula and thus reducing the PVIF. Is it simply that - the reserve at the end of the term of the policy is 0 and thus with all of the reserves released then (because the Vx at the end is 0) it means that it contributes a positive to the profit equation and thereby PVIF increasing ?
Hi The profit formula you have looks ok. A strengthening of the reserving basis will reduce profits because the amount of reserve that you need relative to the reserves that you have has now increased. This however is historic profit (that has arisen over the reporting year) and so causes an impact (reduction) to your free assets and not your VIF, which is forward looking. As you correctly state, the higher reserves will increase your VIF as the prudence in the reserves generate profit for the insurer over the product's lifetime. (the impact on EV will depend on the net impact on these opposing forces). Your query regarding reserves that increase over time isn't clear. However remember that reserves are calculated prospectively. Therefore the 'shape' of the reserves has already been captured within the 'time 0' reserve figure. What happens over the product's lifetime is simply an unwinding of the start position (this is complicated where actual and expected experience diverge or where there is new business so ive ignored it here)
