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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Projecting and valuing cashflows contingent on multiple decrement events

In a double-decrement service table, l_x^(τ) = 10,000 lives are in service at age x. During the year, d_x^(1) = 300 leave by withdrawal and d_x^(2) = 200 leave by death. What is the probability that a life aged x is still in service at age x+1?

The probability is 0.95. Total decrements are 300 withdrawals plus 200 deaths, which is 500 out of 10,000 lives. Survival in service is one minus the total decrement probability of 0.05, so 0.95. Counting only one cause of exit would give a wrong figure.

  1. A0.95Correct
  2. B0.97
  3. C0.98
  4. D0.05
  5. 0.93

Explanation

Total decrements are 300 + 200 = 500. The probability of remaining in service is (p_x)^(τ) = (10,000 − 500)/10,000 = 0.95. The value 0.97 counts only withdrawals as leaving, and 0.05 is the total exit probability rather than the survival probability.

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