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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Transition intensities dependent on age (exact or census)

A life office uses the census method. On 1 January 2023 there were 5,000 policyholders and on 1 January 2024 there were 5,200, and the investigation is for calendar year 2023. Using the trapezium rule on the two census counts to approximate the central exposed to risk, and 60 deaths in the year, what is the estimated mortality intensity?

Under the trapezium rule the central exposed to risk is the average of the two census counts, 5,100 life-years over one year. Dividing 60 deaths by 5,100 gives an estimated mortality intensity of 0.01176.

  1. A60/5,000 = 0.01200
  2. B60/5,100 = 0.01176Correct
  3. C60/5,200 = 0.01154
  4. D60/10,200 = 0.00588
  5. 60/5,150 = 0.01165

Explanation

The trapezium rule gives exposure = (5,000 + 5,200)/2 x 1 = 5,100 life-years. Intensity = 60/5,100 = 0.01176. Using a single census count gives other options which are wrong.

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