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

Which statement about mortality profit for a portfolio of one-year term assurance policies is correct, given a DSAR that is positive for every policy?

With a positive death strain at risk, mortality profit equals expected deaths minus actual deaths, multiplied by the DSAR. So it is positive when fewer deaths occur than expected, and negative when more occur than expected.

  1. AMortality profit is positive when actual deaths exceed expected deaths
  2. BMortality profit is zero whenever the reserve equals the premium
  3. CMortality profit is positive when actual deaths are fewer than expected deathsCorrect
  4. DMortality profit depends only on the number of survivors, not on the DSAR
  5. Mortality profit is negative when actual deaths are fewer than expected deaths

Explanation

Mortality profit = EDS - ADS = (expected deaths - actual deaths) × DSAR when DSAR is common. With a positive DSAR, fewer actual deaths than expected gives a positive profit. The other statements reverse the sign or ignore DSAR.

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