Unfortunately it doesn't work!
Your middle state fails the definition of the Markov property; "the probability of being in a future state depends only on the current state occupied". Remember we are working in one year intervals and not 2-year intervals.
So the states are:
S0: Starting state with no claims. If you don't claim, you stay.
S1: You arrive here from S0 if you claim in previous year.
S2: You arrive here from S1 if you claim in previous year. If you claim again, you stay.
S1-: You arrive here from S2 if you have a claim-free year. Alternatively, arrive from S1 if you don't claim. Then if you claim, go to S1. If you don't claim go to S0.
So the states are set up now based on one-year cycles and one-year histories - which is necessary to satisfy Markov definition when working in single years.
In the attached image; C = Claim & N = No-claim.
Don't be too sad though, I bet you pick up a lot of marks for your working on the rest of the question.
And I could always be wrong of course.
I was hoping it might be 48%.
Note to acted: If you like you can use my attached graph in your asset solutions next year It's quality!
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Last edited by a moderator: Sep 7, 2006