IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Mortality projection
In a Lee-Carter model, log m(x,t) = a(x) + b(x)k(t) + ε(x,t). Which statement about the parameters is correct?
In the Lee-Carter model, b(x) measures how sensitive log mortality at age x is to changes in the period index k(t). Parameter a(x) is the average age profile and k(t) is the time index that is forecast.
- Aa(x) is the period index that is forecast using a time series model, and b(x) is the average age profile
- Bb(x) measures the sensitivity of the log mortality rate at age x to changes in the period index k(t)Correct
- Ck(t) is an age-specific constant that captures the average log mortality at each age
- Db(x) is the cohort effect for people born in year t − x
- a(x) measures the speed of mortality improvement at age x
Explanation
In Lee-Carter, a(x) is the average age pattern of log mortality, k(t) is the time-varying index usually forecast with a random walk with drift, and b(x) shows how strongly each age responds to changes in k(t). The other options swap these roles or introduce a cohort term that the basic model lacks.
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