Actuarial Outpost Expectation Curtate Future Lifetime
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#11
09-17-2018, 12:24 PM
 windsowe Member SOA Join Date: Feb 2011 Location: Nashville Studying for MLC College: Vanderbilt Alum Favorite beer: Lucky Bucket IPA Posts: 205

It's 6.3 from the LTAM 165:

Stuart, now age 65, purchased a 20-year deferred whole life annuity-due of 1 per year at age 45.
You are given:
(i) Equal annual premiums, determined using the equivalence principle, were paid
at the beginning of each year during the deferral period.
(ii) Mortality at ages 65 and older follows the Standard Ultimate Life Table.
(iii) i = 0.05
(iv) Y is the present value random variable at age 65 for Stuart’s annuity benefits.
Calculate the probability that Y is less than the actuarial accumulated value of Stuart’s
#12
09-17-2018, 12:27 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,930

Quote:
 Originally Posted by windsowe I have a question about curtate future lifetime. In question 6.3 of the LTAM MC 165, why do we had 1 to the curtate future lifetime of the 65 year old? Why wouldn't the probablility involved simply a:K(t) of a 65 year old instead of a:K(t)+1 of a 65 year old? Thanks for your help!
Because its an annuity due.
#13
09-17-2018, 12:30 PM
 windsowe Member SOA Join Date: Feb 2011 Location: Nashville Studying for MLC College: Vanderbilt Alum Favorite beer: Lucky Bucket IPA Posts: 205

Ah---that helps a lot!
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#14
09-17-2018, 12:34 PM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College B.A. 1962, Stanford Ph.D. 1965 Posts: 2,719

Quote:
 Originally Posted by windsowe I have a question about curtate future lifetime. In question 6.3 of the LTAM MC 165, why do we had 1 to the curtate future lifetime of the 65 year old? Why wouldn't the probablility involved simply a:K(t) of a 65 year old instead of a:K(t)+1 of a 65 year old? Thanks for your help!
Count how many payments are made, depending on K. If K = 0, for example, so that T=0.xxx, then 1 payment was made. And 1 = 0 + 1. In general, K+1 payments are made.
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