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IAI Actuarial Core Principles · Economic Modelling · Role of insurance in reducing or removing risk

An insurer pools n independent policies, each with the same loss distribution of mean m and standard deviation s. Which statement about the loss per policy is correct as n increases?

With independent identical policies, the average loss per policy keeps mean m, but its standard deviation is s divided by the square root of n. Risk per policy therefore diminishes as the pool grows, which is the basis of pooling, although the total risk still grows.

  1. AIts standard deviation falls in proportion to 1/n
  2. BIts mean falls in proportion to 1/sqrt(n)
  3. CIts standard deviation stays at s because losses are independent
  4. DIts standard deviation falls in proportion to 1/sqrt(n) while the mean stays at mCorrect
  5. Both its mean and standard deviation rise in proportion to sqrt(n)

Explanation

Average loss per policy has mean m and variance s^2/n, so standard deviation s/sqrt(n). Option A uses 1/n, which would apply to variance, not standard deviation.

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