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?

\text{ }

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

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

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

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

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

\text{ }

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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?

\text{ }

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

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

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

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

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

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

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