IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Loss distributions, with and without risk sharing
Claim sizes are gamma with alpha = 3 and lambda = 0.01 (rate). After 50% uniform inflation, what is the new mean claim size?
The new mean claim size is 450. The original gamma mean is 3 divided by 0.01, which is 300, and a 50% uniform inflation multiplies it by 1.5, equivalent to dividing the rate parameter by 1.5.
- A200
- B300
- C450Correct
- D600
- 150
Explanation
The original mean is alpha/lambda = 3/0.01 = 300. Inflation of 50% multiplies the mean by 1.5, giving 450; equivalently the new rate is 0.01/1.5 and the mean is 3 x 150 = 450. The option 300 ignores inflation and 600 doubles the mean.
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