Actuarial Outpost m-thly UDD annuities question
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#1
03-02-2019, 07:11 PM
 BartimaeusOfUruk SOA Join Date: Nov 2017 Location: Iowa Studying for FAP Posts: 17 Blog Entries: 3
m-thly UDD annuities question

Under the UDD assumption we know:
-> a-double dot (m) = alpha(m)*a-double dot - beta(m)

Is there another relationship between like this one for the second moment of a monthly annuity under the UDD assumption?

Thanks so much!
#2
03-03-2019, 01:00 AM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College B.A. 1962, Stanford Ph.D. 1965 Posts: 2,705

Quote:
 Originally Posted by BartimaeusOfUruk Under the UDD assumption we know: -> a-double dot (m) = alpha(m)*a-double dot - beta(m) Is there another relationship between like this one for the second moment of a monthly annuity under the UDD assumption? Thanks so much!
Why would you want this, when the variance of the a-double-dot(m) random variable looks just like the formula for the variance when m = 1, except you put a superscript m on every term?
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#3
03-05-2019, 07:02 PM
 BartimaeusOfUruk SOA Join Date: Nov 2017 Location: Iowa Studying for FAP Posts: 17 Blog Entries: 3

I'm unable to find the variance of a monthly annuity given a-double dot, the second moment of a-double dot, and the interest rate. Could you elaborate on the formula you are mentioning please? Thanks so much.
#4
03-05-2019, 07:18 PM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College B.A. 1962, Stanford Ph.D. 1965 Posts: 2,705

Quote:
 Originally Posted by BartimaeusOfUruk I'm unable to find the variance of a monthly annuity given a-double dot, the second moment of a-double dot, and the interest rate. Could you elaborate on the formula you are mentioning please? Thanks so much.
I meant the formula for the variance in terms of Ax and double-force Ax and the discount rate d. Just replace each by its mthly version.

When you say you are given "the second moment of a-double dot", do you really mean the second moment? I suspect that you mean that you are given double-force a-double dot, which is quite different, from which you can easily get double-force A. And are you given these for annual annuities or mthly annuities? I need to know exactly what you're given. Perhaps you could state the problem precisely.
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