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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. Group A: 500 lives, death strain at risk Rs 3,00,000 each, q = 0.01. Group B: 300 lives, death strain at risk Rs 6,00,000 each, q = 0.02. Actual deaths were 4 in Group A and 7 in Group B. What is the total mortality profit or loss?

The portfolio shows a net loss of Rs 3,00,000. Group A gains Rs 3,00,000 from one fewer death than expected, while Group B loses Rs 6,00,000 from one extra death, and the net is a loss of Rs 3,00,000.

  1. AProfit Rs 6,00,000
  2. BLoss Rs 6,00,000Correct
  3. CLoss Rs 3,00,000
  4. DProfit Rs 3,00,000
  5. Loss Rs 9,00,000

Explanation

Group A: expected deaths 5, actual 4, profit = 1 x 3,00,000 = +3,00,000. Group B: expected deaths 6, actual 7, so loss = 1 x 6,00,000 = -6,00,000. Net = 3,00,000 - 6,00,000 = -3,00,000, which is a loss of Rs 3,00,000, so check: option 3 matches this net result. Option 2 ignores Group A's gain.

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