

FlashChat  Actuarial Discussion  Preliminary Exams  CAS/SOA Exams  Cyberchat  Around the World  Suggestions 
LongTerm Actuarial Math Old Exam MLC Forum 

Thread Tools  Search this Thread  Display Modes 

#1




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!
__________________
Former Disney World Cast Member, currently no idea what I'm doing "I think you should refrain from quoting yourself. It sounds pompous."  SweepingRocks 
#2




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:
__________________
Jim Daniel Jim Daniel's Actuarial Seminars www.actuarialseminars.com jimdaniel@actuarialseminars.com 
#3




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)/(10345) = 1/(10345)
__________________
"I'm tryin' to think, but nuthin' happens!" 
#4




Dumb question that I should know the answer to: does that mu equation apply all the time or just when deaths are uniform?
__________________
Former Disney World Cast Member, currently no idea what I'm doing "I think you should refrain from quoting yourself. It sounds pompous."  SweepingRocks 
Thread Tools  Search this Thread 
Display Modes  

