Skip to content

IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Mortality projection

In a Lee-Carter model, k(t) is modelled as a random walk with drift: k(t+1) = k(t) + d + e(t). Fitted k(2020) = -10 and the estimated drift d = -1.5. For age x, b(x) = 0.02 and ln m(x,2020) = -5.30 (equal to a(x)+b(x)k(2020)). What is the projected m(x,2024) using the expected value of k(2024) and ignoring error terms?

Four years of drift reduce k by 6, from -10 to -16. Multiplying by b(x) = 0.02 lowers log mortality by 0.12, so ln m(x,2024) = -5.42 and the projected rate is exp(-5.42).

  1. Aexp(-5.42)Correct
  2. Bexp(-5.36)
  3. Cexp(-5.24)
  4. Dexp(-5.60)
  5. exp(-5.33)

Explanation

Expected k(2024) = -10 + 4(-1.5) = -16, a change of -6. Change in ln m = 0.02 x (-6) = -0.12. So ln m = -5.30 - 0.12 = -5.42. Using only one year's drift gives -5.33, which is wrong.

Did you get it right without looking?

One question tells you little. A timed set on Mortality projection shows your real accuracy, how long you take and where you lose marks.

Practise Mortality projectionFree diagnostic mock

More Mortality projection questions