IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Mortality projection
To make the Lee-Carter model identifiable, a standard pair of constraints is applied. Which pair is correct?
The usual constraints are that b(x) sums to 1 across ages and k(t) sums to 0 across years. These remove the scale and location indeterminacy between b and k, and make a(x) equal the time-average of log mortality at each age.
- ASum of a(x) = 0 and sum of k(t) = 1
- BSum of b(x) = 1 and sum of k(t) = 0Correct
- CSum of b(x) = 0 and sum of k(t) = 1
- DSum of a(x) = 1 and sum of b(x) = 0
- Sum of b(x) = 1 and sum of a(x) = 0
Explanation
The model is unchanged if b is multiplied by c and k divided by c, or if a constant is shifted between a and k. Setting sum of b(x) = 1 fixes the scale and sum of k(t) = 0 fixes the location, making a(x) the average of log m(x,t) over time.
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