Difference between the two methods
I wanted to confirm my understanding of the two methods, as it seems there is a timing difference.
All amounts below relate to AY's t-1 and prior.
(a) = discounted unpaid claims at time t-1 - paid claims during time discounted to time t-1 - unpaid claims at time t discounted to time t-1
Therefore, this calculation is done at time t-1
(b) discounted unpaid claims at t-1 + adjustment for investment income earned during CY t on assets supporting unpaid claims - paid claims at time t - discounted unpaid claims at time t
For (b) it seems like the investment income is bringing the unpaid claims from t-1 to the time value of money at time t and so this calculation is done at time t.
Is this a fair observation or am I misunderstanding the two methods?
Comments
I have thought about this a bit further an I think (b) is more intuitive when you write it this way:
It has 2 components:
(1) discounted unpaid at time t-1
(2) discount unpaid at time t + paid claims at time t
We can bring (2) back to time t-1 by subtracting the investment income earned during CY t on assets supporting the unpaid claims
(2*) discount unpaid at time t + paid claims at time t - adjustment for investment income during year t
because the formula is (1)-(2*) we end up adding the adjustment for investment income due to a double negative
Final formula:
= discounted unpaid claims at t-1 + adjustment for investment income earned during CY t on assets supporting unpaid claims - paid claims at time t - discounted unpaid claims at time t
Yup you are correct there. I have nothing to add