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 the usual choice?
The usual constraints are that b(x) sums to one over ages and k(t) sums to zero over time. The first fixes the scale trade-off between b and k, the second fixes the location, so a(x) becomes the time-average of log mortality.
- ASum of a(x) equals zero and sum of k(t) equals one
- BSum of b(x) equals one and sum of k(t) equals zeroCorrect
- CSum of b(x) equals zero and sum of k(t) equals one
- DEach b(x) equals zero and k(t) is unconstrained
- Sum of a(x) equals one and sum of b(x) equals zero
Explanation
Without constraints, b(x) can be scaled by c and k(t) by 1/c, and k(t) can be shifted with a(x) adjusted. Setting the sum of b(x) to 1 fixes scale, and setting the sum of k(t) to 0 fixes location. Then a(x) is the average of log m(x,t) over time.
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