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

In a Healthy-Sick-Dead model, 30 H to S transitions, 10 H to D transitions and 20 S to D transitions are observed. Time in H totals 1,000 years and time in S totals 250 years. Assuming constant intensities, which statement is correct?

The intensities are 30/1000 = 0.03, 10/1000 = 0.01 and 20/250 = 0.08. The chance that a healthy life leaves first to Sick is 0.03 divided by 0.04, which is 0.75.

  1. AEstimated H to S intensity 0.030, H to D 0.010, S to D 0.080, and the estimated probability that a healthy life's first exit is to Sick is 0.75Correct
  2. BEstimated H to S intensity 0.030, H to D 0.010, S to D 0.080, and the probability a healthy life's first exit is to Sick is 0.30
  3. CEstimated H to S intensity 0.030, H to D 0.010, S to D 0.020, and first exit to Sick probability 0.75
  4. DEstimated H to S intensity 0.030, H to D 0.010, S to D 0.080, and first exit to Sick probability 0.25
  5. Estimated H to S intensity 0.040, H to D 0.010, S to D 0.080, and first exit to Sick probability 0.75

Explanation

H to S = 30/1000 = 0.03, H to D = 10/1000 = 0.01, S to D = 20/250 = 0.08. The first exit from H is to S with probability 0.03/(0.03+0.01) = 0.75. Using 0.30 ignores the competing exit; 0.25 is the probability of going to Dead.

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