BUS3018F: Chapter 6 Summary

Chapter 6
Summary
T -
future lifetime of newborn person


Tx future lifetime of X
person aged
-




w -



limiting age

Rate of
Mortality
Fx (t) = Pr Tx ← t
=
t 9✗

f-✗ (t) =
t Px llxtt
.




Survival Probabilities

S ✗ (t ) = Pr Tx > t
=
I -

Fx (t ) >
t Px = I -



tax
=
t P*

Consistency condition : set Px =
s Px .
t Poets

-
Sot µx+s .
ds
t Px =
e


> used often .

, >
transitioning
Instantaneous rate of
from alive to dead state
Force of
Mortality
him
'

n Pr Tx < t -1h Tx > t
µ×
= , o




complete Expectation of life

W - X



éx = E ( Tx ) =
So + Px .
dt


Curate Lifetimes

Kx = Tx
value of Tx
largest integer
=




> discrete over ( o to w -
x




PMF of Kx : Pr Kx = k =
KPX .
9×+14
=
K Cfx


curtate Expectation of life
W - X



ex = I kpx
K=I