Chpt.5, retrospective reserve

[Ark raw]

Hi,
I'm back with another doubt. This time I'm kinda confused about retrospective reserves. Now coming to the confusion I have.
When I read section 6.4 retrospective reserves, It seemed to me that retrospective reserves are
{accumulated money in} - {accumulated money out}, where accumulation is done of all the past payments (in the form of premium by policy holder and benefits by the insurer) made since the inception of contract till the present day and accumulated to the present day.
1.) Now if my understanding is correct then why do we use EPV expression (like A'_x:t], a"_x:t], etc) for calculating the accumulated values of income
and outgo, because if we are accumulating funds from the past, then we should be certain about the status of life and how much premium we
have received in past and how much we have paid out as benefits. Thus why can't we just simply accumulate it using the formulae we have learned in annuities in ct1 (like using, P*s"_t], for calculating the premiums)?
2.) If my understanding is wrong, then what is the correct description of retrospective reserve?
3.) This doubt that I have is from section 6.5, the very 1st condition that is laid for the equality of retrospective and prospective reserve says that both reserves are same when calculated on the same basis. But if my understanding is correct why do we need a basis for calculation of retrospective reserves?

P.S. a.) we know that basis mentioned in the 3 question is a set of assumptions about mortality and interest rate.
b.) for my question 1.), you can see that the solution of question 5.12, and core reading on page 23 use EPV expressions for calculating accumulated values.
c.) I have read a couple of threads that helped me understand the meaning of retrospective reserve, b ut didn't address the doubt I've raised.

Thank you

 

[Robert Chadburn]

Hi Ark Raw
As far as CT5 is concerned, we need to think of a retrospective reserve as the amount of money that would be accumulated from the past income, on average for each person surviving to the reserving date, on the basis of an assumed experience over the period. We can then base the accumulation on the expected values that are generated from this assumed past experience.

Yes, we can also calculate retrospective reserves on the basis of actual past experience of homogeneous groups of policyholders. This is referred to as the asset share of the policy.

However, even in this case, we can't use compound interest functions like the ones you describe. The point is that a retrospective reserve has to be viewed on the basis of our policy being part of large group of similar policyholders, all of whom are contributing to the total accumulating fund. When one dies, for example, their death benefit sum assured will be paid out of the fund. This deduction impacts on each of the (remaining) survivors' share of the accumulated fund, so you can't just ignore the impact of these deaths. This is why the formulae used have to take account of the proportion of people dying during the accumulation period at each duration - this is what is achieved by the formulae we use.

Robert