MLC Spring 2007 Question 7

[djsven]

The answer given in the official solutions (and the ASM manual) argues that the premium pattern with the earliest payments must generate the largest accumulated value of premiums (and therefore benefit reserve).

My question is: Doesn't this assume a constant rate of mortality, or am I missing something here? Does the accumulated value of premiums not depend on the survival function?

[StevieB]

Accumulated value of premiums does depend on mortality rate.. I think an example might help you see this...

Lets compare the Accumulated value of $5 paid at time 0 vs paid at time 1, seen at time 3.

using standard notation:

5/(v^3* 3Px) > 5/(v^2* 2Px+1)

you can verify this easily, (write 3Px= Px * 2Px+1 )