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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Assurance and annuity functions involving two lives

Two lives (x) and (y) have independent future lifetimes. A whole life assurance pays a sum assured of Rs 1,00,000 at the end of the year of the first death of the two lives. Which of the following gives the expected present value of this benefit?

The EPV is 1,00,000 times A_xy, the whole life assurance on the joint life status. The joint life status fails at the first death, which is exactly when the benefit is paid. The last survivor function applies only to payment at the second death.

  1. A1,00,000 × A_xy, where A_xy is the whole life assurance function on the joint life status (xy)Correct
  2. B1,00,000 × A_x̄ȳ, where the status is the last survivor
  3. C1,00,000 × (A_x × A_y)
  4. D1,00,000 × (A_x + A_y)
  5. 1,00,000 × (A_x − A_y)

Explanation

Payment on the first death is governed by the joint life status (xy), which fails at the first death. So the EPV is 1,00,000 A_xy. The last survivor status would pay only at the second death. The sum or product of single life assurances does not describe the first-death payment.

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