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

For two lives (x) and (y), the complete expectations of life are e_x = 30 years and e_y = 25 years, and the expected time to the first death is 20 years. What is the expected time, in years, until the second death (the last-survivor status)?

The expected time to the second death is 35 years. The first and last death times sum to the two individual lifetimes, so the last-survivor expectation equals 30 + 25 − 20 = 35. The value 55 omits the subtraction of the joint-life expectation.

  1. A35Correct
  2. B15
  3. C55
  4. D25
  5. 45

Explanation

Since T_xy + T_x̄ȳ = T_x + T_y, the expectations satisfy e_x̄ȳ = e_x + e_y − e_xy = 30 + 25 − 20 = 35. The value 55 comes from forgetting to subtract the joint-life expectation.

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