Q13.10

How was calc "cost of increase in reserves"?

end year reserves / interest on reserves / cost of increase in reserves
P / 0 / -P
P / 0.07P / (P-P)+0.07P=0.07P
0 / 0.07P/ (P-0)+0.07P=1.07P

 

I've got that it s using the probability of surviving. i.e. for the 1st year...

the reserve at the start of 1st year is \(V_0 =0 \) and at the end should be \(V_1 = P\). however, not all policyholders survive during the first year, the probability of survive is \({}_1 p_{60}=0.9920\). Moreover, there are no interests earned on reserves since \(V_0=0\), therefore the cost of increasing the reserve during the 1st year is \[ V_0 - V_1 = 0-0.9920P = -0.9920P\] for in-force policyholders. what about year 2 though?

 

http://www.acted.co.uk/forums/showthread.php?t=1724

 

Hi! The link is no longer available now. Anyone could help to answer the question stated above?

 

Hi Siew,
Expected Value of increase in reserve at the end of the year for policies active at start of the year is...
...[reserve at start of the year + interest earned on it - Expected Value of reserve hold at end]

For 2nd year, P×1.07 - (p_61)xP
For 3rd year, Px1.07 - (p_62) x0