Actuarial Outpost
 
Go Back   Actuarial Outpost > Exams - Please Limit Discussion to Exam-Related Topics > SoA/CAS Preliminary Exams > Long-Term Actuarial Math
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions



Long-Term Actuarial Math Old Exam MLC Forum

Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 08-18-2018, 05:52 PM
home_alone home_alone is offline
Member
 
Join Date: Nov 2008
Posts: 428
Default From 2018 LTAM Supplementary Note, Example 5.1

For the endowment benefit why you cannot use the formula: A_bar45:10 = 1-d*a_bar45:10 with the adjusted delta here. The explanation the author provided is even more confusing. Does anyone knows.

Thanks
Reply With Quote
  #2  
Old 08-18-2018, 08:36 PM
Liar Liar is offline
Member
SOA
 
Join Date: Jul 2018
Studying for LTAM
Posts: 311
Default

That adjusted delta isn't the actual interest rate. It's the fake delta when you combine the .04 interest rate and the +.01 force of mortality. They do this to express the probability portions of the annuity using the unadjusted probabilities.


As for the official explanation, it's just a side commentary about how the adjusted force of delta alone can't be used to get the value of insurances. That A* you see on the left-hand side contains both the adjusted interest rate as well as the adjusted probabilities of death from the +.01 force of mortality. This is in contrast to the annuity side, which can exist using the adjusted interest rate and the unadjusted probabilities.

Ex: (v*)(Px) = (v)(Px*). Notice how the probability components of the annuity don't change if you use the adjusted interest rate.
However, (v^[K + 2])(Px*)(q[x + 1]*) DOES NOT equal (v^[K + 2]*)(Px)(q[x + 1]), since the adjusted interest can only transform Px* to the unadjusted form.

The term insurance components in that insurance take the form of (v[k + 2]*)(Px)(q[x + 1]*), which is not the same as using only the adjusted interest rate, since the q term is also adjusted by the new force of mortality.

If you are still having issues comprehending, then I would recommend you just memorize. Memorization is how everyone passes.
Just ace the multiple choice and pull random shit out of your ass in the written answer section.

Last edited by Liar; 08-18-2018 at 10:11 PM..
Reply With Quote
  #3  
Old 08-19-2018, 01:53 AM
home_alone home_alone is offline
Member
 
Join Date: Nov 2008
Posts: 428
Default

Thank you "Liar" for your explanation. I followed your argument but I am not getting the same answer as the book. For a*45:20 I am getting 12.571 but the book apparently got 12.89554.
Here are some details:
a*45:20 = (Integral 0 to 20) of (v^t)(tp*45)dt with v^t=exp(-ln(1.04)*t) and
tp*45=exp(-At-B*c^45*(c^t-1)/ln(c)) with A=.00022+.01+ln(1.04), B=2.7*10^-6, c=1.124. Using Wolfram Alpha I evaluated the integral to be 12.571.
Do you see anything I am doing wrong here.
Reply With Quote
  #4  
Old 08-19-2018, 02:05 AM
Liar Liar is offline
Member
SOA
 
Join Date: Jul 2018
Studying for LTAM
Posts: 311
Default

=/

I'll check later when I have time. I honestly don't think calculating something like this will be on the exam. They'll probably just give you the annuity value using the adjusted interest rate.
Reply With Quote
Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

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 11:05 PM.


Powered by vBulletin®
Copyright ©2000 - 2019, Jelsoft Enterprises Ltd.
*PLEASE NOTE: Posts are not checked for accuracy, and do not
represent the views of the Actuarial Outpost or its sponsors.
Page generated in 0.25591 seconds with 11 queries