IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Concepts of survival models
A lifetime has constant force of mortality μ = 0.02 per year. What is the probability that a life aged 40 survives to age 55?
The survival probability is exp(−0.30). With a constant force of 0.02, the cumulative hazard over the 15 years from age 40 to 55 is 0.30, and survival is the exponential of the negative cumulative hazard.
- Aexp(−0.20)
- Bexp(−0.30)Correct
- Cexp(−0.40)
- Dexp(−0.55)
- 1 − exp(−0.30)
Explanation
Survival over 15 years is exp(−∫μ dt) = exp(−0.02 × 15) = exp(−0.30). With a constant force, age does not matter. Option 1 − exp(−0.30) is the probability of death, not survival.
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