Actuarial Outpost test for given survival functions
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#1
04-07-2005, 10:52 PM
 Sox34 Member Join Date: May 2004 Posts: 1,147
test for given survival functions

So, if a function is given and we're asked to see if it can serve as a force of mortality, the tests are
1. must always be positive, (although not necessarily increasing which was key for last fall's CAS exam)
2. the integral from 0 to infinity of the function must equal infinity

What are the corresponding tests if a function is given and we need to test if it can serve as a survival function?
1. must be [0,1]
some of the other things I've thought of do not work for certain mortality laws.
Anyone know the general rules?
#2
04-07-2005, 10:55 PM
 Sox34 Member Join Date: May 2004 Posts: 1,147

I think I have written down somewhere that s(x) has to be increasing although I do not know if that makes sense to me...
#3
04-07-2005, 11:15 PM
 wat? Member SOA Join Date: May 2004 Location: Hi Studying for FRM Exam Posts: 27,359

Quote:
 Originally Posted by Sox34 I think I have written down somewhere that s(x) has to be increasing although I do not know if that makes sense to me...
• s(x) must be non-increasing. [You can't have a better chance of survival as you get older. (Well, not theoretically - there is the anomaly of newborns.)]
• s(0) = 1
• lim (x-->inf) s(x) = 0
• s(x) is right-continuous
__________________
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#4
04-07-2005, 11:17 PM
 Sox34 Member Join Date: May 2004 Posts: 1,147

Quote:
 Originally Posted by wat? [list][*]s(x) must be non-increasing. [You can't have a better chance of survival as you get older. (Well, not theoretically - there is the anomaly of newborns.)]
yeah i must have had a brainfart when i wrote that down. thanks.
#5
04-08-2005, 07:22 AM
 TwinsFan1987 Member SOA Join Date: Jun 2003 Location: Chicago Studying for FSModules/waiting for APM College: Northwestern College (IA) alumnus Posts: 676

Quote:
 Originally Posted by wat? s(x) must be non-increasing. [You can't have a better chance of survival as you get older. (Well, not theoretically - there is the anomaly of newborns.)]
Actually, the condition doesn't mean that you have a lesser chance of dying as you get older. Many real-life mortality tables account for the high infant mortality rate but still have decreasing survival functions.

What the decreasing (actually non-increasing) survival function means is that no one can be added to the pool - once you die, you're out. If the survival function is level over a time period, then that means that no one dies during that period.

I hope that this helps.
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Quote:
#6
04-08-2005, 09:42 AM
 wat? Member SOA Join Date: May 2004 Location: Hi Studying for FRM Exam Posts: 27,359

Quote:
 Originally Posted by TwinsFan1987 Actually, the condition doesn't mean that you have a lesser chance of dying as you get older. Many real-life mortality tables account for the high infant mortality rate but still have decreasing survival functions. What the decreasing (actually non-increasing) survival function means is that no one can be added to the pool - once you die, you're out. If the survival function is level over a time period, then that means that no one dies during that period. I hope that this helps.
Thanks. My mistake that I didn't check it too carefully - was on my way out of the office.
__________________
"Mathematical Induction: How mathematicians manage to suck all the fun out of lining up a row of dominos, knocking the one on the end down, and watching the entire row fall." -BC
Skip it. - AG

Because everything should taste like bacon.
AO Golfers Unite! Here and here.

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