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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Estimation procedures for lifetime distributions

In an investigation over one year of age, the initial exposed to risk is 400 and 12 deaths are observed. The central exposed to risk is calculated as 394. The initial exposure is usually larger than the central exposure here because:

Initial exposed to risk counts a life who dies during the year as exposed for the full year, whereas central exposed to risk includes only the time actually lived. Hence the initial figure is larger by roughly the unexpired time of those who die, about 6 here.

  1. AThe initial exposure counts those who die as exposed for the full year, while the central exposure counts only the time actually livedCorrect
  2. BThe central exposure includes lives entering after the start of the year
  3. CThe initial exposure ignores withdrawals from the investigation
  4. DThe central exposure includes deaths twice
  5. The initial exposure is measured in lives per year of age rather than time

Explanation

Initial exposure treats each death as if the life had survived to the end of the year, so a death contributes a full year. Central exposure counts only time actually lived. The difference is roughly the unlived time of those who die, here about half of 12 deaths = 6.

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