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

A portfolio has two groups of policies, each with death benefit paid at the end of the year of death. Group A has 2,000 policies with q = 0.002 and death strain at risk Rs 4,00,000 each. Group B has 500 policies with q = 0.010 and death strain at risk Rs 1,00,000 each. During the year Group A had 3 deaths and Group B had 6 deaths. What is the total mortality profit or loss?

The mortality profit is Rs 3,00,000. Expected death strain is Rs 21,00,000 across both groups, while actual death strain is Rs 18,00,000. Total deaths match expectation at nine, but the deaths fell more heavily in the group with the lower strain at risk, creating a profit.

  1. AZero
  2. BProfit of Rs 3,00,000Correct
  3. CLoss of Rs 3,00,000
  4. DProfit of Rs 2,10,000
  5. Loss of Rs 18,00,000

Explanation

EDS: A = 2,000 x 0.002 x 4,00,000 = 16,00,000; B = 500 x 0.01 x 1,00,000 = 5,00,000; total 21,00,000. ADS: 3 x 4,00,000 + 6 x 1,00,000 = 18,00,000. Profit = 21,00,000 - 18,00,000 = 3,00,000. Comparing only total deaths (9 expected, 9 actual) would wrongly give zero.

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