Tag Archives: Inverse Gamma Distribution

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}

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