Skip to content

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

A two-state-exit model observes 400 life-years in state A. During this exposure, 20 transitions from A to B and 30 transitions from A to C were recorded. Assuming constant intensities, what are the maximum likelihood estimates of mu_AB and mu_AC, and what is the estimated probability that a life in A stays in A for 2 years?

The estimates are mu_AB = 20/400 = 0.05 and mu_AC = 30/400 = 0.075. The total exit rate is 0.125, so the probability of remaining in A for 2 years is exp(-0.25) ≈ 0.779. The value 0.221 is the complementary probability.

  1. A0.05 and 0.075; 0.779Correct
  2. B0.05 and 0.075; 0.882
  3. C0.05 and 0.075; 0.905
  4. D0.0625 and 0.0625; 0.779
  5. 0.05 and 0.075; 0.221

Explanation

MLE of each intensity is transitions divided by waiting time: 20/400 = 0.05 and 30/400 = 0.075. Total exit intensity 0.125, so the 2-year stay probability is exp(-0.25) = 0.7788, i.e. 0.779. The 0.882 option uses 0.0625 per year, and 0.221 is the complement.

Did you get it right without looking?

One question tells you little. A timed set on Transition intensities dependent on age (exact or census) shows your real accuracy, how long you take and where you lose marks.

Practise Transition intensities dependent on age (exact or census)Free diagnostic mock

More Transition intensities dependent on age (exact or census) questions