IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Markov processes
A time-homogeneous Markov jump process has states 0 and 1 with generator matrix rows (-3, 3) and (2, -2). What is the expected holding time in state 0 on each visit?
The expected holding time in state 0 is 1/3. The holding time is exponential with rate equal to the total force of leaving state 0, which is 3, so its mean is the reciprocal of that rate.
- A1/2
- B1/3Correct
- C1/5
- D3
- 2/3
Explanation
The holding time in a state is exponential with rate equal to the total transition rate out of it. For state 0 the rate is 3, so the mean holding time is 1/3. The value 1/2 is the mean holding time in state 1, which uses the wrong row.
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