IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Markov processes
A healthy-sick two-state model has constant rates: healthy to sick 0.2 per year and sick to healthy 0.6 per year. The process is in the healthy state at time 0. Which is the long-run probability of being in the sick state?
The long-run probability of being sick is 0.25. Balancing flows, 0.2 times the healthy probability equals 0.6 times the sick probability, so healthy is three times sick, giving sick one quarter of the total.
- A0.20
- B0.25Correct
- C0.33
- D0.75
- 0.60
Explanation
Stationary probabilities satisfy pi_H*0.2 = pi_S*0.6, so pi_H = 3 pi_S. With pi_H + pi_S = 1, pi_S = 1/4 = 0.25. The value 0.75 is the healthy probability, from reading the answer for the wrong state.
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