Exam C Practice Problem 26 – A Limited Fluctuation Credibility Example

Problem 26-A

You are given the following about a large portfolio of insurance policies:

• For each insurance policy, the annual number of claims follows a binomial distribution with $m$ = 3 and $q$ = 0.3.
• The claim size follows an inverse Gamma distribution with $\alpha$ = 2.1 and $\theta$ = 3.
• The number of claims and the claim sizes are independent.
• The full credibility standard has been selected so that actual claim costs will be
within 10% of expected claim costs 90% of the time.

Using limited fluctuation credibility, determine the expected number of claims required for full credibility.

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 460$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 790$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2895$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3715$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4600$

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Problem 26-B

You are given the following about a large portfolio of insurance policies:

• For each insurance policy, the annual number of claims follows a binomial distribution with $m$ = 6 and $q$ = 0.1.
• The claim size follows a Gamma distribution with $\alpha$ = 0.8 and $\theta$ = 1.
• The number of claims and the claim sizes are independent.
• The full credibility standard has been selected so that actual claim costs will be
within 10% of expected claim costs 90% of the time.

Using limited fluctuation credibility, determine the expected number of exposures required for full credibility.

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 514$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 582$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 970$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5141$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5818$

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$\copyright \ 2013 \ \ \text{Dan Ma}$