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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Gross random future loss

For a policy with gross random future loss L, which statement correctly defines the 95th percentile premium?

The 95th percentile premium is the smallest premium for which the probability of a positive future loss is at most 5%. This means the insurer avoids a loss with at least 95% probability. It is not the equivalence premium, which sets the expected loss to zero.

  1. AThe premium that makes the expected value of L equal to zero
  2. BThe largest premium for which the probability that L is positive is at least 5%
  3. CThe premium that makes the standard deviation of L equal to 5% of the sum assured
  4. DThe smallest premium for which the probability that L is positive is at most 5%Correct
  5. The premium that makes L equal to zero in 95% of cases and positive in the remaining 5%

Explanation

The percentile premium is the smallest premium P for which Pr(L > 0) is no more than 5%, so the insurer makes a profit with at least 95% probability. Setting E[L] = 0 gives the equivalence premium, which is a different principle. The other options mix up the direction of the inequality or invent a standard deviation condition.

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