IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Markov processes
In a three-state model (Healthy 0, Sick 1, Dead 2) with constant transition rates, the rate 0 to 1 is 0.10, 0 to 2 is 0.02 and 1 to 2 is 0.20. Recovery is not possible. What is the probability that a life healthy now is still healthy after 2 years?
The probability of still being healthy after 2 years is exp(-0.24), about 0.787. The total rate out of the healthy state is 0.12 and with no recovery, remaining healthy means never leaving, so the survival probability is exponential in 0.12 times 2.
- Aexp(-0.24) = 0.787
- Bexp(-0.12) = 0.887Correct
- Cexp(-0.20) = 0.819
- D1 - 0.12 x 2 = 0.760
- exp(-0.10) = 0.905
Explanation
Total rate out of state 0 is 0.10 + 0.02 = 0.12. Since there is no return to 0, the probability of staying in 0 for 2 years equals exp(-0.12 x 2) = exp(-0.24) = 0.787. Option 1 omits the factor of 2 in the exponent.
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