Exam C Practice Problem 23 – Working with Credibility Estimates

Both Problems 23-A and 23-B use the following information.

You are given the following:

  • A portfolio of independent risks is divided into two classes.
  • Each class contains the same number of risks.
  • For each risk in Class 1, the claim size follows a zero-truncated geometric distribution with mean 1.5.
  • For each risk in Class 2, the claim size follows a zero-truncated geometric distribution with mean 2.5.
  • See definition of zero-truncated distribution here.

A risk is selected at random from the portfolio. The first claim observed for this risk is 3.

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Problem 23-A

Calculate the Bayesian credibility estimate of the expected value of the next claim that will be observed for this risk.

\text{ }

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.00

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.10

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.16

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.20

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.30

\text{ }

\text{ }

\text{ }

\text{ }

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Problem 23-B

Calculate the Buhlmann credibility estimate of the expected value of the next claim that will be observed for this risk.

\text{ }

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.00

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.10

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.16

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.20

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.30

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\text{ }

\text{ }

\text{ }

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\text{ }

\text{ }

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

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