Tag Archives: Limited Fluctuation Credibility

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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Exam C Practice Problem 20 – Working with Full Credibility Standard

Problem 20-A

You are given the following:

  • The annual number of claims generated from a portfolio of insurance policies follows a Poisson distribution.
  • The claim size is modeled by the random variable Y=X^2 where X has an exponential distribution with mean 2.
  • 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 5% of expected claim costs 95% of the time.

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

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      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3073

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4610

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6147

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 7684

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 9220

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Problem 20-B

You are given the following:

  • The annual number of claims generated from a portfolio of insurance policies follows a Poisson distribution.
  • The claim size is modeled by the random variable Y=4 X^2+32 where X has an exponential distribution with mean 2.
  • 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 5% of expected claim costs 95% of the time.

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

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      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2017

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3073

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3457

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4150

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 9220

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

Exam C Practice Problem 14 – Examples of Limited Fluctuation Credibility

Problem 14-A

You are given the following:

  • The annual number of claims generated from a portfolio of insurance policies follows a Poisson distribution.
  • The claim size follows a uniform distribution on (0,t) where t is unknown.
  • The number of claims and the claim sizes are independent.

Using limited fluctuation credibility, how many expected claims are required to be 95% certain that actual claim costs will be within 5% of the expected claim costs?

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      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1443

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1579

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1936

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1945

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2050

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Problem 14-B

You are given the following:

  • The annual number of claims generated from a portfolio of insurance policies follows a Poisson distribution.
  • The claim size follows a distribution with the following moment generating function.
    • \displaystyle M(t)=\frac{1}{(1-10t)^4}
  • The number of claims and the claim sizes are independent.

What is the least number of expected claims that are required to be 90% certain that actual claim costs will be within 5% of the expected claim costs?

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      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 820

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1230

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1353

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1376

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1396

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