Initial exposed to risk

Hi everyone,

A quick question: X was born 4/2/1990; joined study 1/3/2012; study commenced 1/1/2012. X dies 1/4/2012; study ends 31/12/2012. What is X's contribution to INITIAL exposed to risk age 22 (E sub 22)?
Some explanation would be appreciated, thanks guys!

 

As X became 22 on 4/2/2012 , but he joined study on 1/3/2012
So we count from 1/3/2012 , but he died on 1/4/2012...
And we know Initial exposed to risk at age x for \(D_i=1 \) is from x+a_i to x+1
Hence we count from 1/3/2012 to 3/2/2013..... 366-31-29+31+3
Therefore \( E_{22}=340 \)

 

Thanks but study ended 31/12/2012

 

The deaths contribute the period of length 1 -a_i from x+a_i to x+1 :-See pg.no. 12 of Chapter 10
Here x+1 is 4/2/2013 hence calculated till 3/2/2013

 

Yes, that is what the book says but there was no reference to end of investigation scenario. Please can one of the Acted tutors answer this. Thanks!

 

Here is the reference:- solution 4.9 part (ii) of Q&A bank 4.
Please, any ActEd tutor corfirm it to him.

 

I think that every death should contribute "1 yr" to the initial exposed to risk (Ex). Reason?

For example -
A study started 1 Jan 15 and ended 1 Jan 16. A person, whose birthday is on 1 Feb, entered the study on 1 March.
Now he died after 3 months i.e. on 1 Jun. His contribution to Ex is from 1 march 2015 to 1 Feb 2016 i.e. 11 months

So our estimate of qx = 1 / (11/12) > 1 !

Is there any flaw in my thinking?

 

As far as I understand, E_x=11/12.
But for getting Actuarial Estimate, E_x should taken as 1.

PS:- Chapter:Binomial & Poisson models has been changed.