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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Markov processes

In a time-homogeneous Markov jump process with states Healthy (H), Sick (S) and Dead (D), the transition rates are constant. Which statement about the holding time in state H is correct?

The holding time in state H is exponential, with parameter equal to the total of all transition rates out of H. This follows from the memoryless property of a time-homogeneous Markov jump process, so a single transition rate alone is not enough.

  1. AIt follows an exponential distribution with parameter equal to the sum of the transition rates out of HCorrect
  2. BIt follows an exponential distribution with parameter equal to the rate of the most likely transition out of H
  3. CIt follows a Weibull distribution with shape parameter 2
  4. DIt is uniform between 0 and 1 year
  5. It follows a gamma distribution with parameter equal to the number of states

Explanation

In a time-homogeneous Markov jump process, the waiting time in a state is exponential with rate equal to the total force of transition out of that state. The other options use a single rate or an unrelated distribution, which does not follow from the Markov property.

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