IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Transition intensities dependent on age (exact or census)
In a two-state model a life has constant force of mortality mu = 0.02 per year at all ages. What is the probability that a life aged 40 survives to age 55, to 4 decimal places?
With a constant force of 0.02, survival over 15 years is exp(-0.02 times 15) = exp(-0.3), which equals 0.7408. The survival probability is the exponential of minus the integrated force of mortality.
- A0.7408Correct
- B0.3000
- C0.8187
- D0.6065
- 0.7000
Explanation
15p40 = exp(-0.02 x 15) = exp(-0.30) = 0.7408. Option 0.3000 wrongly multiplies mu by t and treats it as a probability. 0.8187 is exp(-0.2), using 10 years. 0.6065 is exp(-0.5), using 25 years.
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