IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Mortality projection
An actuary uses a mortality reduction factor approach: q(x,t) = q(x,0) × [alpha(x) + (1 - alpha(x)) × (1 - f(x))^(t/n)]. With alpha(x) = 0.4, f(x) = 0.5, n = 20, what is the ratio q(x,20)/q(x,0)?
At t equal to 20 the exponent is 1, so the bracket is 0.4 + 0.6 × 0.5 = 0.70. Mortality at that time is 70% of the base rate, since alpha = 0.4 is the proportion that never improves.
- A0.70Correct
- B0.50
- C0.90
- D0.20
- 0.60
Explanation
At t = n = 20, the exponent is 1, so (1 - f) = 0.5. The ratio is 0.4 + 0.6 x 0.5 = 0.4 + 0.3 = 0.70. The value 0.5 wrongly ignores alpha, the floor on improvement.
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