IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Mortality projection
In Lee-Carter projections, k(t) is often modelled as a random walk with drift, k(t+1) = k(t) + d + e(t). If the fitted drift d is -1.5 and k(2024) = -20, what is the central forecast of k(2029)?
The central forecast of k(2029) is -27.5, because a random walk with drift has expected value equal to the current value plus the number of steps times the drift: -20 + 5 x (-1.5) = -27.5.
- A-27.5Correct
- B-21.5
- C-18.5
- D-30.0
- -20.0
Explanation
Five steps ahead the expected value is k(2024) + 5d = -20 + 5(-1.5) = -27.5. Using only one step gives -21.5, a common error. Using +7.5 gives -12.5, and ignoring drift gives -20.
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