Hi all In ch5, section 5 talks about restrospective accumulations. The expected AV of benefits is derived here. I got the formuale derived in sec 5.1 but got stuck in sec 5.2. As they have already considered the random variable of AV of benefit and did its expectation, then why we need to divide it by npx? The expectation of AV of benefits is expressed as (1+i)ⁿ A¹x:-n and this is what we need. Then why npx is here? Could anyone please explain? Thanks
Here we are calculating EPV @ given time from starting time. So we are 1st calculating PV @ time 0 and then accumulating it over given period. For PV of payment certain, the accumulating factor is (1+I)^n And for EPV ( (1+I) ^n * surviving probability i.e nPx Now we need to multiply by (1+i)^n/nPx or in simple term multiply by ( Dx/Dx+n)
Accumulations in CT5 are always defined in terms of the amount of money accumulated per survivor. That is, we take the money that's accumulated in the bank and share it out between the survivors at time n. Imagine in your example that we have 1000 people at the start, aged x. The accumulated amount in total would be: 1000 (1+i)ⁿ A¹x:-n We then divide the total amount by the expected number surviving to time n, which would be 1000 nPx. So we get (1+i)ⁿ A¹x:-n / nPx altogether (the 1000 cancels). Robert
