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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Maximum likelihood estimators for transition intensities

In a three-state model (Healthy H, Sick S, Dead D) observed over a period, there were 20 transitions H to S, 10 transitions H to D and 30 years total time spent in H. Assuming constant intensities, what is the estimated probability that a life currently in H stays in H for one year (the survival probability in state H)?

The total exit intensity from H is the sum of 20/30 and 10/30, which equals 1.0, so the estimated probability of staying in H for a year is exp(-1.0). Using only one of the two exit intensities would understate the total force of leaving.

  1. Aexp(-1.0)Correct
  2. Bexp(-0.667)
  3. Cexp(-0.333)
  4. Dexp(-1.5)
  5. exp(-2.0)

Explanation

Estimated mu_HS = 20/30 = 0.6667 and mu_HD = 10/30 = 0.3333. Total force of leaving H is 1.0. The one-year probability of remaining in H continuously is exp(-1.0). Using only one intensity gives the distractors exp(-0.667) or exp(-0.333).

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