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in BUS 3024S - Contingencies by (1.6k points)

Hi, how would your answer to (ii) change if there was a transition from Critically ill to healthy? I realize in this case they just used the holding probabilities and the non-holding interchangeably since no return is possible. 

Also, if there was no limit on the bounds i.e. if they asked for the probability of the policyholder becoming ill in the future (no age specified) would the last probability (staying in state 1) have a term of infinity? (infP:t+25)

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1 Answer

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by (2.9k points)
Then it would be a normal Healthy-Sick-Dead model expression (because the idea with H-CI-D is that once you leave the healthy state, you can't come back).

In this case, you would put in the expression integral_{0}^{20}(tP^(01)_45)dt and would need to solve from there. I would start by finding the expression using the Kolmogorov's forward/backward equations and then integrate from there but it seems a little messy. I think it would be good for you to attempt it and post your attempt for us to check (when you get a moment). 
by (1.6k points)
Would the only change be that the holding probability in state one would now include the force of transition back to the healthy state? i.e. 0.01 + mu^10?
by (2.9k points)
Kind of. You would then need another transition back into the critically state. Remember, its the probability that at age 65 the person must be in the critically sick state (so they can move back and forth between the healthy and sick state as many times as they like between then).