IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Stochastic processes
A two-state Markov jump process has states A (active) and B (inactive). The rate from A to B is 0.2 per year and from B to A is 0.6 per year. What is the long-run proportion of time spent in state A?
The long-run proportion in A is 0.75. Balance of flows requires πA times 0.2 to equal πB times 0.6, so πA is three times πB, and with probabilities summing to one this gives πA of 0.75.
- A0.25
- B0.33
- C0.60
- D0.75Correct
- 0.80
Explanation
Stationary distribution satisfies πA·0.2 = πB·0.6, so πA = 3πB. With πA+πB=1, πA = 0.75. Option 0.25 is πB, the inverted answer.
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