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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Valuing cashflows contingent on multiple transition events

In a disability income model with states Healthy (H), Sick (S) and Dead (D), a life is Healthy now. Constant forces are: H to S 0.08, H to D 0.02, S to D 0.05, and no recovery. Which expression gives the probability of being in state H at time t?

The probability of still being Healthy at time t is e^{-0.10t}. Staying in Healthy means avoiding every exit, so the total exit intensity 0.08 plus 0.02 is used. Intensities from the Sick state do not affect it.

  1. Ae^{-0.08t}
  2. Be^{-0.10t}Correct
  3. Ce^{-0.15t}
  4. D1 - e^{-0.10t}
  5. e^{-0.02t}

Explanation

Remaining in H requires no exit by any route, and the total exit force is 0.08+0.02 = 0.10. Hence tpHH = e^{-0.10t}. e^{-0.08t} ignores death from H. e^{-0.15t} incorrectly includes the S to D intensity.

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