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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Transition intensities dependent on age (exact or census)

In a continuous-time multiple state model, the transition intensity from state i to state j (i ≠ j) at age x is defined as mu_ij(x) = lim h→0 of P(State j at x+h | State i at x) / h. Which statement about this quantity is correct?

A transition intensity is an instantaneous rate, the limit of the transition probability divided by the time interval. It is non-negative but can exceed 1, because it is a rate per unit time rather than a probability, and it need not fall with age.

  1. AIt is a probability and must lie between 0 and 1
  2. BIt is a rate that can exceed 1 and is non-negativeCorrect
  3. CIt is always a decreasing function of age
  4. DIt equals the probability of being in state j at age x+1
  5. It must sum to 1 across all states j for a given i

Explanation

A transition intensity is a limiting probability per unit time, so it is a non-negative rate, not a probability. It can exceed 1 and need not decrease with age. The intensities out of a state do not sum to 1.

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