IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Mortality projection
A projection uses mortality rates q(x,t) = q(x,0) × R(x,t), with R(x,t) = [1 − f(x)]^t where f(65) = 2% per year. Rates at age 65 in the base year are 0.010000. What is the projected q(65,10), to 6 decimal places?
The projected rate is 0.008171. Apply the reduction factor 0.98 for each of 10 years: 0.98^10 is about 0.81707, and multiplying by the base rate 0.010000 gives 0.008171. A linear 20% cut would wrongly give 0.008000.
- A0.008000
- B0.008171Correct
- C0.008179
- D0.008204
- 0.012190
Explanation
0.98^10: 0.98^2=0.9604; ^4=0.92237; ^8=0.85076; ^10=0.85076×0.9604=0.81707. Multiply by 0.010000 gives 0.008171. The 0.008000 option uses a simple linear 20% cut; 0.012190 wrongly uses 1.02^10.
Did you get it right without looking?
One question tells you little. A timed set on Mortality projection shows your real accuracy, how long you take and where you lose marks.
More Mortality projection questions
- To make the Lee-Carter model identifiable, a standard pair of constraints is applied. Which pair is correct?
- To make the Lee-Carter model identifiable, a standard pair of constraints is applied. Which pair is the usual choice?
- 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)?
- In a stochastic mortality projection model, which statement best describes the difference between process risk and parameter risk?
- Lee-Carter k(t) is modelled as a random walk with drift: k(t+1) = k(t) + d + e(t), where e(t) is independent N(0, s²). Estimated d = -1.5 an…
- In the Lee-Carter model ln m(x,t) = a(x) + b(x)k(t), the period index k(t) is typically projected forward using which approach?