Have a ques... April 04, 103 Ques 3

[MindFull]

Hi guys I just wanted to know for this question why is the transition rate for the members of the scheme who die (mu)n?
Also, why does the forward equation have a minus sigh infront of the first part of the eqn.?

Thanks a lot.

Here's the link (First one is the exam paper, next is the exam report)
http://www.actuaries.org.uk/files/pdf/pastpapers/2004apr/103x_a04.pdf

http://www.actuaries.org.uk/files/pdf/pastpapers/2004apr/103r_a04.pdf

 

[MindFull]

no repliess....

Hi!

Is there a reason why noone is answering my question from the past paper?
Any reply would be appreciated. Thanks.

 

[Robert Chadburn]

Hi
The rate at which N(t) is increasing by 1 is given as lambda, regardless of what the value of N(t) is. But the rate at which N(t) is decreasing is expressed as the rate mu per life. So if N(t)=1, the rate at which one death would be occurring would be mu. But if N(t)=n, the rate at which 1 death would be occurring would be n-times faster than this, ie n(mu).

pn is the probability of staying in the same state n. The forward d.e for pn is:

- Sum(all rates of leaving the end state n) x pn + Sum(all rates of entering the end state n from all other states) x p(other state)

This is the same form as the general eqn shown on page 33 of the Tables. The first part of the equation in this question is second part of the equation in the tables! - that's all.

Can you see it now? Shout again if you can't.
(I'm not around again till thursday though - but someone else could have a go?)
Enjoy.

 

[MindFull]

Thanks.

Thanks much!!