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

Claim amounts X follow a Pareto distribution with parameters alpha = 4 and lambda = 600 (in rupees thousand). Claims inflate uniformly by 10% over a year. Which statement describes the distribution of the inflated claims?

The inflated claims are Pareto with alpha = 4 and lambda = 660. Pareto is a scale family, so a 10% uniform inflation multiplies the scale parameter lambda by 1.1 to 660, while the shape parameter alpha remains unchanged at 4.

  1. APareto with alpha = 4 and lambda = 660Correct
  2. BPareto with alpha = 4.4 and lambda = 600
  3. CPareto with alpha = 3.6 and lambda = 660
  4. DPareto with alpha = 4 and lambda = 545.5
  5. Pareto with alpha = 4.4 and lambda = 660

Explanation

Pareto is a scale family where lambda is the scale parameter. Multiplying claims by 1.10 multiplies lambda by 1.10, giving 660, while alpha (the shape) stays 4. Changing alpha or dividing by 1.10 mixes up shape and scale or reverses the direction of the inflation.

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