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Smash Puny Human
02-21-2002, 08:55 AM
From HTP3 pg 141, exercise 4.
You are given that delta = 0 and that mort follows deMoivre's law with
omega = 105. A special continuous life annuity is issued to a lide aged 25
with a payment rate of b_sub_t =2*t. the present value random variable for
this annuity is Y. Find the variance of Y. (Answer: You must find the first
two moments of Y using the Aggregate Payment Technique. Y(t) = T^2. The
first two moments are 2133.33 and 8,192,000, so that the variance is
3,640,889.)

I can find the first moment, but am having trouble with the second. Maybe I
do not understand the Agg. Pay Tech. Any help would be appreciated. Thanks.

BCNU
02-27-2002, 05:03 PM
The density of deaths is 1/80, due to the DeMoivre assumptions. As you said, you got the first moment just fine.

The first is E[Y]=Integral[t^2(dt/80)]=80^2/3

The second is E[Y^2]=Integral[(t^2)^2(dt/80)]=80^4/5

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<font size=-1>[ This Message was edited by: BCNU on 2002-02-27 17:05 ]</font>