WHY is it this way and not the other way around!!!!!

[The Mighty Gorgon]

The retrospective way for calculating reserve at t is:

acc value of premiums - cost of insurance (or acc value of Ax)

But isnt it the other way around?

like loss at issue = Gain of insured - Premium payed as an annuity

and retrospective way is just looking at that at a different time, so why not:

acc value of insurance - acc value of premiums?

Why is it the other way? The manual doesnt explain.

Thanks.
Grrr.

[d123454321]

It is

Accumulated premiums - Acc cost of insurance

because at time 10 say, when you have more accumulated premiums than insurance payouts (cost of insurance) you have a surplus, AKA a reserve at time 10.


This reserve occurs because (prospectively), at time 10 after having a excess built from time 0-10, now from 10 and on, the present value of benefits will exceed the present value of future premiums so the reserve is needed to cover this future loss.

The retrospective formula comes from the prospective, but in the opposite fashion.

If in the past you had a reserve (negative loss), then in the future you will have positive loss (negative reserve)

*assuming equivalence principle*

[Gandalf]

Here's a similar situation in an FM context.

You are borrowing 10,000 from the bank and repaying it over 10 years. What is the balance at the end of year 4?

Prospectively, it is the PV of the future payments from you. Which we could also say it is the PV of the future payments from you - the PV of the future amounts from the bank (that latter term is 0).

Can we do it retrospectively? Sure. Which of these ways to you want to do it:

Accum value of payments from you - Accum value of amounts from the bank

or

Accum value of amounts from the bank less Accum value of payments from you.

In the both the FM case and the MLC case, you can start with

PV of payments by you, before time t, + PV of payments by you, after time t = PV of payments by company (bank or insurer) before time t + PV of payments by company after time t.

Group the "before time t" on one side, the "after time t" on the other, and you'll see the signs flip.

[Vorian Atreides]

When I sat for this material, I had looked at it from this perspective:

Premiums are the cash available to pay out any obligations . . . cost of insurance is what has already been paid (on average).

You need to work the formula as (Prem - cost of insurance) so that you know how much you have available to invest (i.e., if cost > prem, where did the additional $$ come from?).

[actuary44]

Gandalf: Shouldn't the formula in your post at the end all be "plusses"? Your last sign is a negative....

[Gandalf]

Originally Posted by actuary44

Gandalf: Shouldn't the formula n your post at the end all be "plusses"? Your last sign is a negative....

yes, fixed, thanx

[The Mighty Gorgon]

Thank you Gandalf. I replace the FM concept with MLC.

Equilavelcen principle is what makes it work.

Gotcha! good.