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

In a continuous-time Markov jump process model for a policyholder with states 0 (healthy), 1 (sick) and 2 (dead), which statement about the transition intensity μ01(x) is correct?

The transition intensity is an instantaneous rate: the probability of moving from state 0 to state 1 in a small interval h is approximately h times μ01(x). It is not itself a probability, and under the Markov assumption it does not depend on past duration in the state.

  1. AIt equals the probability of moving from state 0 to state 1 in a year
  2. BIt is the instantaneous rate such that the probability of moving from 0 to 1 in a short interval h is approximately h·μ01(x)Correct
  3. CIt must be less than 1 at every age
  4. DIt equals the sum of all intensities out of state 0
  5. It depends on the time already spent in state 0 under the Markov assumption

Explanation

An intensity is a rate, not a probability: P(0→1 in h) ≈ h·μ01(x) for small h. It can exceed 1, the total exit rate is the sum of all out-intensities (not μ01 alone), and the Markov property means the future depends only on the current state and age, not on the duration spent in it.

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