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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 model, the force of decrement from cause 1 is a constant 0.02 per annum and from cause 2 is a constant 0.03 per annum. What is the probability that a life currently in the population leaves within one year by cause 1?

The probability is 0.0195. With constant forces, the chance of leaving by cause 1 is its share of the total force, 0.02/0.05, multiplied by the probability of any exit in a year, 1 - e^-0.05 = 0.04877.

  1. A0.0195Correct
  2. B0.0198
  3. C0.0200
  4. D0.0488
  5. 0.0293

Explanation

With constant forces the total force is 0.05. The probability of exit by cause 1 within one year is (0.02/0.05)(1 - e^-0.05) = 0.4 x 0.048771 = 0.0195. The value 0.0198 treats cause 1 as if it acted alone, ignoring competition from cause 2. The value 0.0488 is the probability of leaving by any cause.

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