mortality fluctuation reserve

[claire3000006]

In the acted notes (p13/14 of chapter 26) the following process is described:

1. net loss from claims is x = [C(g) - C(r)] - [P(g) - P(r)]
where C(g) is gross claims, C(r) is claims recovered from reinsurer, P(g) is gross premiums received, P(r) is premiums paid to reinsurer

2. cost of mortality fluctuation reserve of size M is M(j-i) where i is expected return from assets that back reserve, j is shareholders' required return

3. if 60% of the reinsurance premiums are used to cover reserve then size of reserve is M = 30P(r) (assuming i=7%, j=9%)

4. net loss is nowX = [C(g) - C'(r)] - [P(g) - P(r)] -M
where C'(r) is claims recovered from reinsurer under new arrangement

my question: why is is still P(r) and not 0.4P(r)? is this just an act ed mistake or is there something i don't understand? surely if you're using that 0.6P(r) to pay for a mortality fluctuation reserve instead then you're no longer paying for the reinsurance as well...?

 

[Mike Lewry]

The clue is in the italics sentence at the top of page 14: "we have exchanged reinsurance for a MFR, at parity of cost"

We're still using up all of P(r). A cost of 0.4P(r) gets us claim recoveries of C'(r) and a cost of 0.6P(r) gets us a MFR of M.

So you could write the net loss as:

X=[C(g)-C'(r)-M]-[P(g)-0.4P(r)-0.6P(r)]

which is the same as in the Notes.

 

[claire3000006]

ah of course, get it now thanks