IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Concepts of survival models
A lifetime has survival function S(t)=(1 - t/100)^2 for 0≤t<100. What is the force of mortality at t=20?
The force of mortality is minus the derivative of ln S(t). Here ln S = 2 ln(1 - t/100), so μ(t)=2/(100-t). At t=20 that equals 2/80=0.025. Ignoring the shrinking denominator would give an incorrect 0.02.
- A0.0250Correct
- B0.0200
- C0.0400
- D0.0100
- 0.0025
Explanation
μ(t) = -d/dt ln S(t) = 2/(100-t). At t=20 this is 2/80=0.025. The 0.0200 option uses 2/100, forgetting to reduce the denominator; 0.04 arises from 2/50.
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