IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Transition intensities dependent on age (exact or census)
In a two-state model, μ_{x+t} = 0.001 + 0.0001t for t ≥ 0 (t in years, from age x). What is the 10-year survival probability from age x, to 4 decimal places?
The 10-year survival probability is e^(-0.015), about 0.9851, because the integrated force over ten years is 0.01 plus 0.005. Using only the constant part gives 0.9900, which ignores the rising term.
- A0.9851Correct
- B0.9900
- C0.9802
- D0.9753
- 0.9950
Explanation
Integral of μ from 0 to 10 = 0.001x10 + 0.0001x(100/2) = 0.01 + 0.005 = 0.015. Survival = e^(-0.015) = 0.98511. Option 1 uses only the constant term (e^-0.01). Option 2 doubles the integral wrongly.
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