IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Mortality projection
In the Lee-Carter model, log m(x,t) = a(x) + b(x)k(t), which of the following is the role of the parameter b(x)?
The parameter b(x) in the Lee-Carter model measures how sensitive log mortality at age x is to movements in the period index k(t). The average age pattern is captured by a(x), while k(t) carries the overall time trend.
- AIt measures the average level of log mortality at age x over the period
- BIt measures the sensitivity of log mortality at age x to changes in the period index k(t)Correct
- CIt measures the cohort effect for lives born in year t-x
- DIt measures the random error at age x in year t
- It measures the linear trend in mortality across all ages equally
Explanation
In Lee-Carter, a(x) gives the average age pattern of log mortality, k(t) is the period index, and b(x) scales how strongly each age responds to changes in k(t). The average level is a(x), not b(x), so that option is wrong.
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