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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Loss distributions, with and without risk sharing

Claims follow a Pareto distribution with parameters alpha = 4 and lambda = 6,000 (Rs). Claims inflate by 25% with no change in alpha. Which pair gives the new Pareto parameters and the new mean claim?

The new Pareto has alpha = 4 and lambda = 7,500, giving a mean of Rs 2,500. Inflation scales lambda by 1.25 while the shape alpha stays fixed, and the mean 7,500/3 equals the old mean of 2,000 times 1.25.

  1. Aalpha = 4, lambda = 7,500, mean = 2,500Correct
  2. Balpha = 5, lambda = 6,000, mean = 1,500
  3. Calpha = 4, lambda = 7,500, mean = 2,000
  4. Dalpha = 4, lambda = 6,000, mean = 2,500
  5. alpha = 3.2, lambda = 6,000, mean = 2,500

Explanation

Scaling a Pareto by 1.25 multiplies lambda by 1.25 and leaves alpha unchanged, so lambda = 7,500. The mean is lambda/(alpha-1) = 7,500/3 = 2,500. Check: the old mean is 2,000, and 2,000 x 1.25 = 2,500. The option with lambda = 7,500 and mean 2,000 forgets to update the mean.

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