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 Short-Term Actuarial Math Old Exam C Forum

#31
06-20-2016, 10:20 PM
 newleaf9413 Member SOA Non-Actuary Join Date: Feb 2016 Location: Minneapolis, MN Studying for C & MFE College: SDA Bocconi Favorite beer: Stout Posts: 30
Question #274

The answered provided by SOA is as follows:

S(x) = e^-H(x)

H(x) = 0.5534 (I got this part.)

Nelson-Aalen Estimate = 1/50 + 3/49 + 5/k + 7/12 = 0.5534

---> k = 36.

Why the last term is NOT 7/21? Did I miss something?

L
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#32
06-20-2016, 10:28 PM
 cammcgra Member SOA Join Date: Jul 2014 Location: Detroit, MI College: University of Michigan Favorite beer: Half Acre Daisy Cutter Posts: 51

Quote:
 Originally Posted by newleaf9413 The answered provided by SOA is as follows: S(x) = e^-H(x) H(x) = 0.5534 (I got this part.) Nelson-Aalen Estimate = 1/50 + 3/49 + 5/k + 7/12 = 0.5534 ---> k = 36. Why the last term is NOT 7/21? Did I miss something? Please let me know at your earliest convenience thanks. L
Hi newleaf, that's just a typo in the solution. The last term is actually 7/21. You'll notice if you plug in k = 35, and correct the last term, the equation sums correctly to .5534
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#33
06-20-2016, 10:46 PM
 newleaf9413 Member SOA Non-Actuary Join Date: Feb 2016 Location: Minneapolis, MN Studying for C & MFE College: SDA Bocconi Favorite beer: Stout Posts: 30

Thank you so much. I'm just trying to remember whatever I can. Wednesday is the day.
#34
07-22-2016, 09:57 AM
 n27 Member SOA Join Date: Oct 2015 Studying for QFI Core Exam Posts: 210

I am struggling with question 70. I was able to get EPV by doing [.2(.5)+.8(1) + .2(.8) + .8(1] /2 . But i cannot get VHM. (2.3-1.8)^2 * .5*.5 which i think is intuitive.
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#35
08-13-2016, 09:03 PM
 mathematicalhype Member CAS SOA Join Date: Nov 2013 Posts: 270

SOA Question 2:
The number of claims has a Poisson Dist.
Claims have a Pareto dist with parameters theta = .5 and alpha =6. The number of claims and claim sizes are independent.
The observed pure premium should be within 2% of the expected pure premium 90% of the time.

Calculate the expected number of claims needed for full credibility.

What key words in this question indicate that we are looking for number of claims needed for full credibility of aggregate losses?
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#36
08-13-2016, 09:35 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,145

#37
08-13-2016, 09:38 PM
 mathematicalhype Member CAS SOA Join Date: Nov 2013 Posts: 270

SOA Question 4:
How is a * 3^(-a-1) * a * 6^(-a-1) * a * 14^(-a-1) * (25^-a)^2
proportional to:
a^3 * (3*6*14*625)^-a

I understand how we get a^3, but I am not sure for the second piece how the exponent for all numbers can be -a when for three of those values, the exponent was (-a-1)?
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#38
08-13-2016, 09:45 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,145

I think you have a type in your last term.
#39
08-13-2016, 10:19 PM
 Actuarialsuck Member Join Date: Sep 2007 Posts: 6,117

Quote:
 Originally Posted by mathematicalhype SOA Question 4: How is a * 3^(-a-1) * a * 6^(-a-1) * a * 14^(-a-1) * (25^-a)^2 proportional to: a^3 * (3*6*14*625)^-a I understand how we get a^3, but I am not sure for the second piece how the exponent for all numbers can be -a when for three of those values, the exponent was (-a-1)?
So you can see how the a^3 is in there right?

So now we have to deal with 3^{-a-1} * 6^{-a-1} * 14^{-a-1} * 25^{-2a} = 3^{-1} * 3^{-a} * 6^{-a} * 6^{-1} * 14^{-a} * 14^{-1} * 625^{-a}

Everything that is not raised to the a'th (or -a'th) power is a constant so hence we can say it's proportional to and you are left with (3*6*14*625)^{-a}
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#40
08-21-2016, 03:19 PM
 mathematicalhype Member CAS SOA Join Date: Nov 2013 Posts: 270

Quote:
 Originally Posted by Actuarialsuck So you can see how the a^3 is in there right? So now we have to deal with 3^{-a-1} * 6^{-a-1} * 14^{-a-1} * 25^{-2a} = 3^{-1} * 3^{-a} * 6^{-a} * 6^{-1} * 14^{-a} * 14^{-1} * 625^{-a} Everything that is not raised to the a'th (or -a'th) power is a constant so hence we can say it's proportional to and you are left with (3*6*14*625)^{-a}
Thank you!
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