IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Assurance and annuity functions involving two lives
Independent lives (x) and (y) have constant forces of mortality 0.02 and 0.03 respectively. Find E[T_x̄ȳ], the expected time until the last death, to two decimal places in years.
The expected time to last death is 63.33 years. Since max = T_x + T_y − min, the expectation is 50 + 33.33 − 20. Omitting the subtraction of the joint-life mean of 20 gives the incorrect 83.33.
- A20.00
- B30.00
- C63.33Correct
- D83.33
- 103.33
Explanation
Use E[last] = E[T_x] + E[T_y] − E[T_xy] = 50 + 33.33 − 20 = 63.33 years. The value 83.33 omits subtracting the joint-life expectation. Check by integrating: ∫(e^-0.02t + e^-0.03t − e^-0.05t)dt = 50 + 33.33 − 20.
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