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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 the limit of which quantity as h tends to 0 from above?

The transition intensity from i to j at age x is the limit, as h shrinks to zero from above, of the probability of being in state j at age x+h given state i at age x, divided by h. It is an instantaneous rate of transition.

  1. Ah × P(state j at age x+h | state i at age x)
  2. BP(state j at age x+h | state i at age x) / hCorrect
  3. CP(state i at age x+h | state j at age x) / h
  4. DP(remain in state i throughout (x, x+h)) / h
  5. 1 − P(state i at age x+h | state i at age x)

Explanation

The intensity is mu_ij(x) = lim of h p_x^{ij} / h as h tends to 0 from above. It is a rate of transition per unit time, so the probability is divided by h, not multiplied. Option 4 relates to staying put, not a transition to j.

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