Actuarial Outpost > CAS Minimum Bias: Fox Problem at page 9b
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#1
09-25-2010, 12:38 PM
 CASPart5 Member Join Date: Aug 2004 Posts: 76
Minimum Bias: Fox Problem at page 9b

The problem is about using Additive Model, Least Squares Method. Fox solution uses a formula based approach. With so many formulae in part9 syllabus already, I'm trying to rely on first principles to solve this problem (rather than memorizing formulae), but for some reason I'm getting a wrong answer below. Can anyone please elaborate what is wrong with my approach:

si: row relativity
hj: column relativity

Initial values: s1 = 130, s2=50

Total losses=
62,500 157,500 30,000
90,000 41,250 112,500

125(200+s1+h1) 350(200+s1+h2) 75(200+s1+h3)
300(200+s2+h1) 150(200+s2+h2) 450(200+s2+h3)

SSE=
(125s1 + 125h1-37,500)^2 + (350s1 + 350h2 - 87,500)^2 +
(75s1 + 75h3 - 15,000)^2 + (300s2 + 300h1 - 30,000)^2 + (150s2 + 150h2 - 11,250)^2
+ (450s2 + 450h3 - 22,500)^2

Partial derivative of SSE w.r.t h1 gives:

2(125s1 + 125h1 - 37,500)(125) + 2(300s2 + 300h1 - 30,000)(300) = 0

Putting initial values of s1 and s2 in above equation, we get:

h1= 67.7514

However, fox's formula based solution comes up with h1=85.294

Can someone please explain what am I missing here?

Thank you so much for your time.
#2
09-25-2010, 04:41 PM
 CtrlAltDelete Member CAS Join Date: Jun 2007 Studying for CAS 9 Posts: 1,187

Quote:
 Originally Posted by CASPart5 SSE= (125s1 + 125h1-37,500)^2.
The bold should be 75,000. I didn't bother checking the rest, you should do it yourself.
#3
09-25-2010, 05:29 PM
 CASPart5 Member Join Date: Aug 2004 Posts: 76

Thanks CtrlAltDelete!

The way I'm getting 37,500 is:

125*200: from Total Indicated Pure Premium
MINUS
62,500: from Total losses

Can you please elaborate how did you get 75,000?

Thanks,
#4
10-07-2010, 02:25 PM
 Jing.only Member Join Date: Jan 2009 College: University of Wisconsin-Madison Posts: 43

I am confused by this question too.
But I figured out a way to get the answer

if you take the lost cost and reduce the base rate to get a (300 250 200 100 75 50) with (x1+y1 X1+y2 X1+y3 X2+y1 x2+y2 X2+y3)
sse=125*(x1+y1-300)^2+350*(x1+y2-250)^2+.....
then you will get the same answer...
#5
10-07-2010, 03:03 PM
 CASPart5 Member Join Date: Aug 2004 Posts: 76

thanks Jing! for taking time & answering...
#6
10-07-2010, 03:10 PM
 llcooljabe Member CAS Join Date: Aug 2002 Favorite beer: Rickard's Red Posts: 14,367

I clicked on this thread before looking at the subsection. I thought this was political and the topic was Fox News. Carry on.

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