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#31
10-27-2017, 10:02 PM
 hunkal Member SOA Join Date: Feb 2015 Posts: 35

Quote:
 Originally Posted by mel.fel yeah sick or healthy so i did 1-p(dead). since it seemed easier
Did you get .1335 or phi(-1.101)?

Tha wasn't an answer. I must have calculated my probabilities wrong. What was the answer you got if you remember?
#32
10-27-2017, 10:04 PM
 ngxxx081 Member SOA Join Date: Nov 2008 Posts: 107

Quote:
 Originally Posted by mel.fel i did prob of being sick at the beg of year 3 (so two time periods) then 1000*prob and variance is 1000*(1-prob)*prob and then did the normal approx. it wasn't four because i struggled with four.. and i remember totally guessing that.
It was #3 - one thing I didn't catch at first was that you wanted the probability of being alive (healthy OR sick, but NOT dead) at the BEGINNING of t=3 which is the end of t=2. I was calculating probability of being healthy only which and combining sick with dead. After realizing the syntax error I corrected my calculations and got something that made more sense and one of the answer choices.
#33
10-27-2017, 10:05 PM
 hunkal Member SOA Join Date: Feb 2015 Posts: 35

How did you guys calculate the variance of the 10 pay annuity at time 5 where they give you premium is 166.5 or something? This was one of the written answer, later they ask for covariance of the whole life insurance and term annuity which I also couldn't get

I also couldn't get the premium for the common shock model. Or the pv of the benefit when the guy dies after the girl

Also, what is the Kolmogorov forward differential equation for tpx in state j? Why only one state?

Last edited by hunkal; 10-27-2017 at 10:18 PM..
#34
10-27-2017, 10:20 PM
 ngxxx081 Member SOA Join Date: Nov 2008 Posts: 107

Quote:
 Originally Posted by hunkal How did you guys calculate the variance of the 10 pay annuity at time 5 where they give you premium is 166.5 or something? This was one of the written answer, later they ask for covariance of the whole life insurance and term annuity which I also couldn't get I also couldn't get the premium for the common shock model. Or the pv of the benefit when the guy dies after the girl
The "simpler" approach to calculating variance of an annuity is to look at it in terms of insurance so a_x = [1-A_x]/d; taking the variance of this expression and with a little algebra you get Var((P/d)(1-v^Kx+1)) which can be re-written as Var((P/d)-(P/d)v^Kx+)). Then taking the variance of each of the two items you get:

(P/d)^2*Var(v^Kx+1) (P/d is a constant and variance of a constant is zero).

You will then recognize Var(v^Kx+1) as variance for an insurance item (this was a simplified approach, use appropriate corresponding annuity/insurance relation).

I couldn't prove the premium for the common shock model question - at this point I had lost steam and still had to get to the last question.
#35
10-27-2017, 10:23 PM
 mel.fel Member SOA Join Date: Feb 2017 Posts: 188

Quote:
 Originally Posted by ngxxx081 It was #3 - one thing I didn't catch at first was that you wanted the probability of being alive (healthy OR sick, but NOT dead) at the BEGINNING of t=3 which is the end of t=2. I was calculating probability of being healthy only which and combining sick with dead. After realizing the syntax error I corrected my calculations and got something that made more sense and one of the answer choices.
yeah i caught that too but my brain wasn't working so i ended up going 1-dead, whicha lso worked.
C /#3 sounds right to me,
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#36
10-27-2017, 10:24 PM
 mel.fel Member SOA Join Date: Feb 2017 Posts: 188

Quote:
 Originally Posted by ngxxx081 The "simpler" approach to calculating variance of an annuity is to look at it in terms of insurance so a_x = [1-A_x]/d; taking the variance of this expression and with a little algebra you get Var((P/d)(1-v^Kx+1)) which can be re-written as Var((P/d)-(P/d)v^Kx+)). Then taking the variance of each of the two items you get: (P/d)^2*Var(v^Kx+1) (P/d is a constant and variance of a constant is zero). You will then recognize Var(v^Kx+1) as variance for an insurance item (this was a simplified approach, use appropriate corresponding annuity/insurance relation). I couldn't prove the premium for the common shock model question - at this point I had lost steam and still had to get to the last question.
ha im the opposite. i got the premium but not the variance.
again, just ran out of time. lmao.
__________________
P | FM | MFE | C| MLC
FAP 1 2 3 4 IA 6 7 FA
VEE STATS | VEE FINANCE | VEE ECON
#37
10-27-2017, 10:28 PM
 Demo99 Member SOA Join Date: Jan 2013 Posts: 124

Quote:
 Originally Posted by mel.fel ha im the opposite. i got the premium but not the variance. again, just ran out of time. lmao.
I ended up just writing formulas for this entire question with all the parts, without solving for a single value. Hoping to get at least a few points on this whole thing.
#38
10-27-2017, 10:33 PM
 noone SOA Join Date: Feb 2017 Posts: 23

Quote:
This is correct and the answer was E. The AV without the CF was larger then the AV with the CF which means the CF is in play. The question asked for the ADB which would be 1.5AV. If you did not use the CF and just did ADB = FA - AV you would have got choice A which is not correct.
#39
10-27-2017, 10:40 PM
 ngxxx081 Member SOA Join Date: Nov 2008 Posts: 107

Quote:
 Originally Posted by noone This is correct and the answer was E. The AV without the CF was larger then the AV with the CF which means the CF is in play. The question asked for the ADB which would be 1.5AV. If you did not use the CF and just did ADB = FA - AV you would have got choice A which is not correct.
I thought for these types of problems you went with the method that yielded the higher cost of insurance which for this question I determined it to be without corridor factor, which is it might seem just as many chose FA-AV as those who did AV*(corridor-1).

Of course this was one of last few concepts I started understanding better in the last month so maybe my calculations could have been off.
#40
10-27-2017, 10:41 PM
 cixelsidmaikool Member SOA Join Date: Mar 2016 College: Providence College Posts: 36

yeah, that sounds right (unfortunately). For some reason I keep mixing up AV and COI. higher COI/lower AV = corridor in play, but I flipped it.

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