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September 2008 Q 9

  • Thread starter snerap@gmail.com
  • Start date
I assume you are looking at the solution in the Examiners Report.

Delta here is a short period of time.

Since retirement is compulsory at age 65, anyone who is in state 1 or 2 before age 65 must have transferred to state 4 by (just after) age 65. So tpx11 and tpx12 are 0 for x+t = 65+delta, as no one can remain in states 1 or 2 after 65.

The second equation relates to those people in state 1 at age x. The probability that they are in state 4 just after age 65 (at time 65+delta) is equal to the probability that they are in states 1 or 2 just before age 65 (at age 65-delta), as everyone in states 1 and 2 moves to state 4 at age 65.
 
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