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

Claims are lognormal with mu = 8.0 and sigma = 0.5. Over the next year claims inflate uniformly by 20%. Which describes the inflated claim distribution?

The inflated claims are lognormal with mu = 8.0 + ln(1.2) and sigma still 0.5. Multiplying claims by 1.2 adds ln 1.2 to the log claims, which shifts the mean of the underlying normal without changing its spread.

  1. ALognormal with mu = 8.0 and sigma = 0.6
  2. BLognormal with mu = 8.0 + ln(1.2) and sigma = 0.5Correct
  3. CLognormal with mu = 9.2 and sigma = 0.5
  4. DLognormal with mu = 8.0 + ln(1.2) and sigma = 0.5 x 1.2
  5. Normal with mean 8.0 + ln(1.2)

Explanation

If Y = 1.2X then ln Y = ln X + ln 1.2, a shift of the normal mean by ln 1.2 (about 0.182). The variance of ln Y is unchanged, so sigma stays 0.5. Adding 20% to mu or sigma directly confuses the log scale with the claim scale.

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