IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Concepts of survival models
A survival model has constant force of mortality μ = 0.04 at all ages. What is the complete expectation of life at age 60?
The complete expectation of life is 25 years. With a constant force of mortality 0.04, survival is exponential, so the integral of exp(-0.04t) over all t equals 1/0.04, independent of age.
- A15 years
- B20 years
- C25 yearsCorrect
- D30 years
- 40 years
Explanation
With constant force, S_x(t) = exp(-0.04t). Then e°_60 = ∫ exp(-0.04t) dt = 1/0.04 = 25 years. The value 20 would need μ = 0.05; 40 would not follow from any simple slip except dividing by 0.025.
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