Actuarial Outpost Survival model
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#1
02-24-2014, 10:15 PM
 Akeen Member CAS SOA Join Date: Dec 2012 Studying for FM College: University of Kent Posts: 91
Survival model

Given that a survival model satisfies
S0(x| X < z) = [(z^3) - (x^3)] / [(z^3)*(1 + x^3)]
Find S0(x | z < X) if x > z

The solution:
S0(x) = lim S0(x|X < z) as z -> infinity
= 1/ (1 + x^3)

How did they get this and then how do you finish the question?
#2
02-24-2014, 10:32 PM
 What A Noob Member CAS SOA Join Date: Feb 2014 Studying for MLC College: University of Manitoba Favorite beer: Pepsi Posts: 86

Quote:
 Originally Posted by Akeen Given that a survival model satisfies S0(x| X < z) = [(z^3) - (x^3)] / [(z^3)*(1 + x^3)] Find S0(x | z < X) if x > z The solution: S0(x) = lim S0(x|X < z) as z -> infinity = 1/ (1 + x^3) How did they get this and then how do you finish the question?
If Z is infinity that means it is unconditional.

you are welcome
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#3
02-24-2014, 10:49 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,925

s(x| x > z) = s(x)/s(z) x > z