Actuarial Outpost SOA #85
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#1
05-02-2012, 03:50 PM
 clive Member Join Date: Jan 2007 Posts: 67
SOA #85

To get EPV of benefit at time 2, SOA official solution integrates from 0 to infinity, see attachment, the integration result is 1000* e^0.08.

I am trying to integrate from 2 to infinity, with the formula below. I got 1000* e^-.04 as the result.

∫ (benefit) * (tPx) * (discount factor) * mu

∫ (1000e^.04t) * (e^-02t) * (e^-.04t) * (.02) dt

Apparently something is not correct in my formula, could you tell me how to fix it and your reasoning?

Thanks!
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#2
05-03-2012, 11:37 AM
 Practicing Member SOA Join Date: Sep 2010 Location: NYC Posts: 872

In your formula, when you integrate from 2 to infinity, you are doing it from the perspective of time t = 0. You need to do it from the perspective of time t = 2 because when calculating benefit reserves, we are conditioning on the fact that the life has survived to that time, in this case, t = 2.
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 Originally Posted by Abraham Weishaus I thought the actual exam was very similar to one of the last 2 ASM practice exams, but perhaps those underestimate the difficulty of the exam.
#3
12-28-2017, 04:24 PM
 jdman929 SOA Join Date: Aug 2017 College: University of Wisconsin - Madison Posts: 10

I'm very lost on this problem... Why doesn't this work?

∫ (1000e^.04(t+2)) * (e^-02(t+2)) * (e^-.04(t+2) * (.02) dt from 2 to infinity.

Also in the official solution, what is going on with them breaking up mu(65+t) into mu(65)*t?

Thanks.