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

A policy has a sum assured of Rs 8,00,000 payable at the end of the year of death. The reserve at the start of the year is Rs 2,00,000, the premium net of expenses received at the start is Rs 30,000, and the year-end reserve per surviving policy is Rs 2,40,000. Interest is 5% p.a. and q = 0.01. Using the recursion for a policy where reserves are the same on death or survival, what is the expected death strain per policy at the start of the year?

The death strain at risk uses the year-end reserve, so it is 8,00,000 minus 2,40,000, which is 5,60,000. Multiplying by q of 0.01 gives an expected death strain of Rs 5,600 per policy. Using the opening reserve would be wrong.

  1. ARs 5,600Correct
  2. BRs 5,200
  3. CRs 7,600
  4. DRs 8,000
  5. Rs 6,000

Explanation

DSAR = 8,00,000 - 2,40,000 = 5,60,000. Expected death strain = 0.01 x 5,60,000 = Rs 5,600. Using the opening reserve of 2,00,000 gives 6,000 (wrong base). Interest and premium do not affect it.

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