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

At the start of a year a portfolio has 10,000 identical policies, each with sum assured Rs 2,00,000 payable at the end of the year of death and a year-end reserve of Rs 50,000 per surviving policy. The pricing mortality rate is 0.004. Actual deaths during the year were 52. What is the mortality profit or loss for the year?

There is a mortality loss of Rs 18,00,000. Death strain at risk is Rs 1,50,000, expected deaths are 40 and actual deaths are 52, so the 12 excess deaths cost 12 times 1,50,000. Expected strain is less than actual strain, so the result is a loss.

  1. AProfit of Rs 18,00,000
  2. BLoss of Rs 18,00,000Correct
  3. CLoss of Rs 78,00,000
  4. DProfit of Rs 60,00,000
  5. Loss of Rs 3,60,000

Explanation

DSAR = 2,00,000 - 50,000 = 1,50,000. Expected deaths = 10,000 x 0.004 = 40, so EDS = 40 x 1,50,000 = 60,00,000. ADS = 52 x 1,50,000 = 78,00,000. Mortality profit = EDS - ADS = -18,00,000, a loss because deaths exceeded expectation.

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