IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Mortality projection
A Lee-Carter model is fitted with k(t) following a random walk with drift: k(t+1) = k(t) + d + sigma Z. The fitted drift is d = -1.5, and k(2023) = -4.0. The age-70 parameters are a(70) = -4.2 and b(70) = 0.04. What is the central forecast of m(70, 2025)?
The central forecast is exp(-4.48). Two years of drift take k from -4.0 to -7.0, and log m(70,2025) = -4.2 + 0.04 x (-7.0) = -4.48, so mortality is about 0.0113.
- Aexp(-4.2 - 0.04 x 7) = exp(-4.48)Correct
- Bexp(-4.2 - 0.04 x 4) = exp(-4.36)
- Cexp(-4.2 + 0.04 x 7) = exp(-4.12)
- Dexp(-4.2 - 0.04 x 1.5) = exp(-4.26)
- exp(-4.2 - 0.04 x 5.5) = exp(-4.42)
Explanation
Forecast k(2025) = -4.0 + 2(-1.5) = -7.0. Then log m = -4.2 + 0.04(-7.0) = -4.48. Option 4 uses only one year of drift (-5.5 gives -4.42 is wrong, for k = -5.5). The others misuse the sign or drift.
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