Actuarial Outpost SOA #85
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

 Enter your email to subscribe to DW Simpson weekly actuarial job updates. li.signup { display: block; text-align: center; text-size: .8; padding: 0px; margin: 8px; float: left; } Entry Level Casualty Health Life Pension All Jobs

#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!
Attached Images

#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.
__________________
P FM MFE MLC C VEE IA FA

Quote:
 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: 4

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.

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off

All times are GMT -4. The time now is 09:38 AM.

 -- Default Style - Fluid Width ---- Default Style - Fixed Width ---- Old Default Style ---- Easy on the eyes ---- Smooth Darkness ---- Chestnut ---- Apple-ish Style ---- If Apples were blue ---- If Apples were green ---- If Apples were purple ---- Halloween 2007 ---- B&W ---- Halloween ---- AO Christmas Theme ---- Turkey Day Theme ---- AO 2007 beta ---- 4th Of July Contact Us - Actuarial Outpost - Archive - Privacy Statement - Top