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 01-26-2019, 11:20 PM
SweepingRocks SweepingRocks is offline
Member
SOA
 
Join Date: Jun 2017
College: Bentley University
Posts: 122
Default Term Insurance Question

https://imgur.com/a/wtvpRHh

So that's a link to a question I'm stuck on. I tried using first principles instead of using the shortcut, since the shortcut isn't that intuitive for me. I can understand and calculate the pure endowment part, but for the term insurance this is what I did:

tP45=1-(t/58) and to find the force of mortality between 45 and 65, I took 20P45=.65517=e^(20ux). Then solved for ux as .02114. Then I integrated between 0 and 20 for (1-(t/58))*.02114*(e^.06t), or tP45*ux*v^t.

I ended up with an answer of .28037 for the 20 term insurance, while the solution has .200806. Can someone provide clarity on what I did wrong or why my approach may not work? Thank you in advance!
__________________
FM P MFE STAM LTAM in April

Former Disney World Cast Member, currently no idea what I'm doing

"I think you should refrain from quoting yourself. It sounds pompous." - SweepingRocks
Reply With Quote
  #2  
Old 01-27-2019, 12:08 AM
Jim Daniel's Avatar
Jim Daniel Jim Daniel is offline
Member
SOA
 
Join Date: Jan 2002
Location: Davis, CA
College: Wabash College B.A. 1962, Stanford Ph.D. 1965
Posts: 2,713
Default

You're acting as though mu is a constant, but it's not a constant when you have a uniform distribution on (0, 58) for the future lifetime T_{45}. If you want to use basic principles, note that the density function for T_{45} is the constant 1/58.



Quote:
Originally Posted by SweepingRocks View Post
https://imgur.com/a/wtvpRHh

So that's a link to a question I'm stuck on. I tried using first principles instead of using the shortcut, since the shortcut isn't that intuitive for me. I can understand and calculate the pure endowment part, but for the term insurance this is what I did:

tP45=1-(t/58) and to find the force of mortality between 45 and 65, I took 20P45=.65517=e^(20ux). Then solved for ux as .02114. Then I integrated between 0 and 20 for (1-(t/58))*.02114*(e^.06t), or tP45*ux*v^t.

I ended up with an answer of .28037 for the 20 term insurance, while the solution has .200806. Can someone provide clarity on what I did wrong or why my approach may not work? Thank you in advance!
__________________
Jim Daniel
Jim Daniel's Actuarial Seminars
www.actuarialseminars.com
jimdaniel@actuarialseminars.com
Reply With Quote
  #3  
Old 01-27-2019, 12:13 AM
Breadmaker's Avatar
Breadmaker Breadmaker is offline
Member
SOA
 
Join Date: May 2009
Studying for CPD - and nuttin' else!
College: Swigmore U
Favorite beer: Guinness
Posts: 4,312
Default

The shortcut:

tp45 = l(45+t)/l(45); mu(45+t) =-dl(45+t)/l(45+t)

Multiply and cancel l(45+t) which leaves -dl(45+t)/l(45) = -(-1)/(103-45) = 1/(103-45)
__________________
"I'm tryin' to think, but nuthin' happens!"
Reply With Quote
  #4  
Old 01-27-2019, 10:22 AM
SweepingRocks SweepingRocks is offline
Member
SOA
 
Join Date: Jun 2017
College: Bentley University
Posts: 122
Default

Quote:
Originally Posted by Breadmaker View Post
The shortcut:

tp45 = l(45+t)/l(45); mu(45+t) =-dl(45+t)/l(45+t)

Multiply and cancel l(45+t) which leaves -dl(45+t)/l(45) = -(-1)/(103-45) = 1/(103-45)
Dumb question that I should know the answer to: does that mu equation apply all the time or just when deaths are uniform?
__________________
FM P MFE STAM LTAM in April

Former Disney World Cast Member, currently no idea what I'm doing

"I think you should refrain from quoting yourself. It sounds pompous." - SweepingRocks
Reply With Quote
  #5  
Old 01-27-2019, 11:42 AM
Breadmaker's Avatar
Breadmaker Breadmaker is offline
Member
SOA
 
Join Date: May 2009
Studying for CPD - and nuttin' else!
College: Swigmore U
Favorite beer: Guinness
Posts: 4,312
Default

Applies all the time.
__________________
"I'm tryin' to think, but nuthin' happens!"
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 11:04 AM.


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 0.17335 seconds with 11 queries