IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Mortality projection
A Lee-Carter model is fitted with k(t) forecast as a random walk with drift: k(t+1) = k(t) + d + e(t), where d = −1.5 and e(t) has standard deviation 0.8. Given k(2024) = −20, what are the mean and standard deviation of k(2028)?
The mean is −26 and the standard deviation is 1.6. The mean falls by 1.5 per year over four years, and independent errors add variances: 4 × 0.64 = 2.56, whose square root is 1.6.
- AMean −26, standard deviation 3.2
- BMean −26, standard deviation 1.6Correct
- CMean −21.5, standard deviation 1.6
- DMean −26, standard deviation 0.8
- Mean −23, standard deviation 1.6
Explanation
Four steps ahead: mean = −20 + 4×(−1.5) = −26. Variance = 4×0.8² = 2.56, so the standard deviation = sqrt(2.56) = 1.6. Multiplying 0.8 by 4 (3.2) wrongly assumes the errors are perfectly correlated rather than independent.
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