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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Death strain at risk, expected and actual death strain, mortality profit

An insurer issues one-year term assurance policies. In a given year, the death strain at risk (DSAR) for a policy is defined as the sum assured paid on death in the year less the reserve held at the end of the year. Which expression gives the actual death strain (ADS) for a single policy that was in force at the start of the year?

The actual death strain for one policy equals the death strain at risk (sum assured minus the year-end reserve) if the life dies during the year, and zero if the life survives. Multiplying by the mortality probability would give the expected death strain instead.

  1. AADS = DSAR if the life dies in the year, otherwise ADS = 0Correct
  2. BADS = DSAR for every policy, whether or not death occurs
  3. CADS = q × DSAR, where q is the probability of death
  4. DADS = DSAR if the life survives, otherwise ADS = 0
  5. ADS = sum assured if the life dies, otherwise the reserve

Explanation

Actual death strain is the extra amount needed at the year end because of an actual death: it equals the DSAR (sum assured less end-year reserve) if the life dies and 0 if the life survives. Multiplying by q gives the expected death strain, not the actual one. Option 3 reverses the event.

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