You are given:

1. The number of claims has a Poisson distribution.
2. Claim sizes have a Pareto distribution with parameters [math]\theta = 0.5 [/math] and [math]\alpha = 6[/math]
3. The number of claims and claim sizes are independent.
4. The observed average total payment should be within 2% of the expected average total payment 90% of the time.

Calculate the expected number of claims needed for full credibility.

• Less than 7,000
• At least 7,000, but less than 10,000
• At least 10,000, but less than 13,000
• At least 13,000, but less than 16,000
• At least 16,000

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

Key: E

The standard for full credibility is

[[math]]\left(\frac{1.645}{0.02}\right)^{2}\left(1+\frac{\operatorname{Var}(X)}{\operatorname{E}(X)^{2}}\right)[[/math]]

where [math]X[/math] is the claim size variable. For the Pareto variable, [math]\operatorname{E}(X)=0.5 / 5=0.1[/math] and [math]\operatorname{Var}(X)=\frac{2(0.5)^{2}}{5(4)}-(0.1)^{2}=0.015[/math]. Then the standard is

[[math]]\left(\frac{1.645}{0.02}\right)^{2}\left(1+\frac{0.015}{0.1^{2}}\right)=16,913[[/math]]

claims.

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