A company has determined that the limited fluctuation full credibility standard is 2000 claims if:

1. The total number of claims is to be within 3% of the true value with probability p.
2. The number of claims follows a Poisson distribution.

The standard is changed so that the total cost of claims is to be within 5% of the true value with probability p, where claim severity has probability density function:

[[math]] f(x) = \frac{1}{10,000}, \, 0 \leq x \leq 10,000 [[/math]]

Calculate the expected number of claims necessary to obtain full credibility under the new standard using limited fluctuation credibility.

• 720
• 960
• 2160
• 2667
• 2880

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: B

For the severity distribution the mean is 5,000 and the variance is 10,000² /12 . For credibility based on accuracy with regard to the number of claims,

[[math]] 2000 = \left (\frac{z}{0.03} \right)^2, z^2 = 1.8 [[/math]]

Where z is the appropriate value from the standard normal distribution. For credibility based on accuracy with regard to the total cost of claims, the number of claims needed is

[[math]] \frac{z^2}{0.05^2} \left( 1 + \frac{1000^2/12}{5000^2}\right) = 960. [[/math]]

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.