
Lecture 15
Right-tail behavior of
b
F
n
.
Non-parametric confidence
bounds for expected remaining
life
Consider the expression for the actuarial value of a continuously
payable premium at constant rate p with discounting, which we de-
rived in (12.4):
p
Z
∞
x
e
−ρ(y−x)
1 −F(y)
1 −F(x)
dy.
For small values of x and advanced ages y, say for x = 25 and y ex-
ceeding 80 years, the values of 1 −F(y) seem to play a minor role in
this expression, especially when one considers the discounting taking
place within the integral; and the problem of accurate estimation of F
at high ages does not seem very important.
In practice, however, it rarely happens that the premium established ...