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survival probabilities under constant force of mortality assumption

E

Ex-muso

Member
Q&A Bank 1.5 (ii):

The solution seems to imply the general result (under CFM):

tpx = (px)^t

Should I know that? It's not ringing any bells.
 
I think it's because under constant force of mortality, t_P_x = e^(mu*t) which is equal to (e^mu)^t = (P_x)^t
 
You meant e to power -mu t, but thanks I see what you mean. Sept 09 will also be helpful when I can access a computer which displays it correctly.
 
OK, I've read Q3 from Sept 09 now.

The main answer seems standard. The alternative answer they mention is what you're referring me to, I guess.

This must be an approximation, since under CFM assumption the rate of deaths will slow very slightly over the year, so therefore the half-yr duration survival probability can't be exactly the same from 72 + 1/4 as it is from 72. Right(?).

But it seems they are saying this is an acceptable approximation to use in situations where the whole period in question falls under a single year of age. Anyone agree?
 
I haven't got to this question yet but it seems like an 'unintuitive' approximation.

It implies that tpx < px, which doesn't make sense. The probability of (x) surviving to x+t (0<t<x) is less than the probability of (x) surviving x+1?
 
Plug in some numbers. Let 1px=0.9, and t=0.5. Then under CFM 0.5px=0.9^0.5=0.949. Which makes sense; surviving half a year seems more likely than surviving a full year.
 
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