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

A husband (x) and wife (y), independent lives, buy a policy paying Rs 1 annually in advance while both are alive, reducing to a payment of 2/3 of this level, annually in advance, while only one is alive. Given a_x = 13, a_y = 11, a_xy = 9, what is the expected present value per Rs 1 of the full benefit?

The expected present value is 13.00. The full benefit while both live is worth a_xy = 9, and the two-thirds benefit while exactly one survives is worth (2/3) × (13 + 11 − 18) = 4, giving 13.

  1. A12.00
  2. B14.00
  3. C15.67
  4. D13.00Correct
  5. 16.33

Explanation

Payment 1 while both alive gives a_xy = 9. Payment 2/3 while exactly one alive: the annuity for exactly one is a_x + a_y − 2a_xy = 13 + 11 − 18 = 6. EPV = 9 + (2/3)(6) = 13.00. Using 2/3 on the last-survivor annuity (15) instead would give 9+... wrongly.

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