Why _{0}p_{x}=1?
I'll be grateful for help
Oh of course, I thought it would be enough.
It is :
$\displaystyle _{0}p_{[x]+s}=1$
This is a part of first element of sum:
$\displaystyle \sum_{n=0}^{\infty}\pi_{s+n}v^{n}_{n}p_{[x]+s} $
So what you're asking in this case is...
Given that a person aged 'x' has lived for the previous 's' years, what are the chances they will live at least 0 more years?
That is, 1 - P(they will not live for more than 0 years)..? has to equal 1..
Unless the person in question died while they were filling in the survey.
Yes, thats what I'm asking about.
Well maybe its about it, it would be
$\displaystyle _{0}p_{[x]+s}=1-_{0}q_{[x]+s}$
where $\displaystyle _{0}q_{[x]+s}$ is the conditional probability that a person of x will die in a period of '0' years, on condition that first will live for s years. But how much then is $\displaystyle _{0}q_{[x]+s}$
Suppose you're 57, (which is x in this case ), wanting a pension for when you're 65.
So s in this case would be 8. (Because they're not going to pay that particular pension scheme if you die before you 65th birthday).
The insurance company want to know how likely you are to live for at least n years after your 65th birthday, so they know how much pension you're likely to collect in total before you kick the bucket.
In this case, n is 0.
So the question is: assuming you, 57, live the 8 years until your 65th birthday, what is the probability that you live for at least 0 years after your 65th birthday.
Or the probability that you die within 0 years of your 65th birthday.
(0 years in this case means no time whatsoever. 0 years, 0 months, 0 days, 0 hours, 0 seconds.)
As far as I know.
I could be wrong.
It has happened before.