Actuarial Outpost Multiple Decrement Models
 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

 Long-Term Actuarial Math Old Exam MLC Forum

#1
08-03-2019, 07:08 PM
 isaiahbarrett27 CAS SOA Join Date: Dec 2017 Posts: 10 Blog Entries: 1
Multiple Decrement Models

Hello all! I'm in need of some notation assistance. The notation for the probability of death from 60 to 62 due to any decrement is given as 2q(τ)60. And I've been thinking that q(τ)60 + p(τ)60*q(τ)61 was an analagous formula able to use. However, when I was working through a few life table questions this was given as: # failures due to any decrement between 60 and 62/ I(τ)60. Which should yield the same answer right? But for some reason thats not the case.

Also given:

x l(τ)x d(1)x d(2)x d(3)x
60 1,000 35 65 40
61 l(τ)61 40 d(2)61 35
62 712 51 80 581

where l(τ)61 = 860 and d(2)61 = 73

Last edited by isaiahbarrett27; 08-04-2019 at 11:08 AM..
#2
08-04-2019, 02:46 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,310

What values do those formulas give for 2q(τ)60?
#3
08-04-2019, 11:10 AM
 isaiahbarrett27 CAS SOA Join Date: Dec 2017 Posts: 10 Blog Entries: 1

My answer gives .26728 and theirs .288. Possible just rounding?
#4
08-04-2019, 11:17 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,310

You are likely doing something wrong. Show in steps how you get .26728.
#5
08-04-2019, 11:21 AM
 Breadmaker Member SOA Join Date: May 2009 Studying for CPD - and nuttin' else! College: Swigmore U Favorite beer: Guinness Posts: 5,131

I get 0.288 using your formula.

1000-712 = 288. Just sayin'...
__________________
"I'm tryin' to think, but nuthin' happens!"
#6
08-04-2019, 11:42 AM
 isaiahbarrett27 CAS SOA Join Date: Dec 2017 Posts: 10 Blog Entries: 1

Yep. I'm realizing my error now. Thanks!