## 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.

$\text{ }$

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

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

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

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

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

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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.

$\text{ }$

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

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

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

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

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

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

## Exam C Practice Problem 22 – Estimating Aggregate Claims

Both Problems 22-A and 22-B use the following information.

You are given the following:

• The annual number of claims for a policyholder follows a binomial distribution with mean 0.5 and variance 0.375.
• The following is the probability function of the claim size $X$.
• $\displaystyle \begin{bmatrix} X=x&\text{ }&P(X=x) \\\text{ }&\text{ }&\text{ } \\ 10&\text{ }&0.35 \\ 20&\text{ }&0.35 \\ 30&\text{ }&0.25 \\ 40&\text{ }&0.05 \end{bmatrix}$

• The number of claims and the claim sizes are independent.

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Problem 22-A

Calculate the variance of the annual aggregate claim amount for the policyholder.

$\text{ }$

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 30$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 71.5$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 180$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 190$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 230$

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Problem 22-B

In a certain year, the policyholder has incurred at least one claim and the aggregate claim amount is below 45. Given this information, what is the mean aggregate claim amount for the policyholder?

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 9.0$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 10.0$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 12.5$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 20.0$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 21.3$

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

## Exam C Practice Problem 21 – Working with Aggregate Claims

Problem 21-A

You are given the following:

• The annual number of claims follows a Poisson distribution with mean 800.
• The claim size follows a Gamma distribution with $\alpha$ = 5 and $\theta$ = 2.
• The number of claims and the claim sizes are independent.

Using the normal approximation for the distribution of aggregate claim costs, calculate the probability that the aggregate claim costs will exceed 8350?

$\text{ }$

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.11$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.13$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.15$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.17$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.20$

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Problem 21-B

You are given the following:

• The annual number of claims follows a geometric distribution with mean 8.
• The claim size follows an exponential distribution with mean 5.
• The number of claims and the claim sizes are independent.

Using the normal approximation for the distribution of aggregate claim costs, calculate the 75th percentile of aggregate claim costs?

$\text{ }$

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 64$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 66$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 68$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 70$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 75$

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

## 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?

$\text{ }$

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

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

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

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

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

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

## Exam C Practice Problem 16 – Another Poisson-Gamma Problem

Both Problems 16-A and 16-B use the following information.

A portfolio consists of independent risks divided into two classes. Sixty percent of the risks are in Class 1 and forty percent are in Class 2.

• The annual number of claims for a single risk in Class 1 follows a Poisson distribution with mean 1.
• The claim size follows a Gamma distribution with mean 1.6 and variance 1.28.
• The number of claims and the claim sizes are independent

• The annual number of claims for a single risk in Class 2 follows a Poisson distribution with mean 2.6.
• The claim size follows a Gamma distribution with mean 2.5 and variance 3.125.
• The number of claims and the claim sizes are independent

A risk is randomly selected from this portfolio. According to the records of the insurer, there are 4 claims for this risk in the amounts 2, 3, 5 and 5 within the last 3 years.

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Problem 16-A

Determine the Buhlmann credibility estimate for total claim costs for this risk in the next year.

$\text{ }$

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3.7$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3.7$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4.4$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4.5$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5.0$

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Problem 16-B

Determine the Buhlmann credibility estimate for the number of claims for this risk in the next year.

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.33$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.35$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.46$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.48$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.64$

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

## Exam C Practice Problem 15 – Examples of Frequency-Severity Models

Problem 15-A

You are given the following:

• The annual number of claims generated for a single risk follows a Poisson distribution with mean $\theta$.
• The claim size follows a uniform distribution on $(0,10 \theta)$.
• The risk parameter $\theta$ is a random variable with density function $\displaystyle \pi(\theta)=\frac{1}{2} \ \theta$ where $0<\theta<2$.
• Given $\theta$, the number of claims and the claim sizes are independent.

According to the records of the insurer, there are 4 claims in the amounts 5, 5, 15 and 20 within the last 5 years.

Determine the Buhlmann credibility estimate for total claim costs in the next year.

$\text{ }$

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 9.39$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 9.61$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 9.69$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 10.25$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 10.69$

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Problem 15-B

You are given the following:

• The annual number of claims generated for a single risk follows a Poisson distribution with mean $\theta$.
• The claim size follows a uniform distribution on $(0,100 \theta)$.
• The prior distribution of $\theta$ has a uniform distribution on $(0,5)$.
• Given $\theta$, the number of claims and the claim sizes are independent.

According to the records of the insurer, there are 5 claims in the total amount of 360 within the last 3 years.

Determine the Buhlmann credibility estimate for total claim costs in the next year.

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 97.50$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 164.33$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 179.33$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 212.50$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 257.33$

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

## Exam C Practice Problem 13 – Working with Aggregate Claims

Both Problems 13-A and 13-B use the following information.

A portfolio if independent risks is divided into two classes. Sixty five percent of the risks are in Class 1 and thirty five percent are in Class 2.

The risks in each class are assumed to follow identical annual aggregate claim distribution. The following shows the aggregate claim distributions for the two classes.

$\displaystyle \begin{bmatrix} X=x&\text{ }&P(X=x \lvert \text{Class 1}) &\text{ }&P(X=x \lvert \text{Class 2}) \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ 0&\text{ }&\displaystyle \frac{24}{40} &\text{ }&\displaystyle \frac{4}{12} \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ 5&\text{ }&\displaystyle \frac{6}{40}&\text{ }&\displaystyle \frac{2}{12} \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ 10&\text{ }&\displaystyle \frac{7}{40}&\text{ }&\displaystyle \frac{3}{12} \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ 15&\text{ }&\displaystyle \frac{2}{40}&\text{ }&\displaystyle \frac{2}{12} \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ 20&\text{ }&\displaystyle \frac{1}{40}&\text{ }&\displaystyle \frac{1}{12} \end{bmatrix}$

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Problem 13-A

A risk is randomly selected from this portfolio and is observed to have 15 in aggregate claims in the first year.

What is the probability that the chosen risk will have 15 in aggregate claims in the second year?

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.09$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.10$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.11$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.12$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.13$

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Problem 13-B

A risk is randomly selected from this portfolio and is observed to have 15 in aggregate claims in the first year and 10 in aggregate claims in the second year.

What is the probability that the chosen risk will have 15 in aggregate claims in the third year?

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.09$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.10$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.11$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.12$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.13$

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

## Exam C Practice Problem 12 – Buhlmann Credibility Estimates

Both Problems 12-A and 12-B use the following information.

A portfolio consists of independent risks divided into two classes. Sixty percent of the risks are in Class 1 and forty percent are in Class 2.

• For each risk in Class 1, the number of claims in a year follows a binomial distribution with mean 0.4 and variance 0.32.
• For each risk in Class 1, the size of a claim is 5 with probability 0.6 and 10 with probability 0.4.
• For each risk in Class 1, the number of claims and the claim sizes are independent.

• For each risk in Class 2, the number of claims in a year follows a binomial distribution with mean 1.6 and variance 0.32.
• For each risk in Class 2, the size of a claim is 5 with probability 0.4 and 10 with probability 0.6.
• For each risk in Class 2, the number of claims and the claim sizes are independent.

A randomly selected risk from this portfolio is observed for 3 years. Four claims are incurred in this period (the individual amounts are 5, 5, 5 and 10).

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Problem 12-A

Determine the Buhlmann credibility estimate of the next claim amount of this risk.

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6.25$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6.80$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 7.24$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8.75$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 11.33$

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Problem 12-B

Determine the Buhlmann credibility estimate of the aggregate claims in the next year from this risk.

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6.80$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 7.57$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 7.96$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8.04$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8.33$

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

## Exam C Practice Problem 3 – Bayesian vs Buhlmann

Problem 3-A

A portfolio of independent risks is divided into two classes. Class 1 contains 60% of the risks in the portfolio and the remaining risks are in Class 2.

For each risk in the portfolio, the following shows the distributions of the number of claims in a calendar year.

$\displaystyle \begin{bmatrix} \text{ }&\text{ }&\text{Class 1} &\text{ }&\text{Class 2} \\X=x&\text{ }&P(X=x) &\text{ }&P(X=x) \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ 0&\text{ }&0.50 &\text{ }&0.20 \\ 1&\text{ }&0.25&\text{ }&0.25 \\ 2&\text{ }&0.12&\text{ }&0.30 \\ 3&\text{ }&0.08&\text{ }&0.15 \\ 4&\text{ }&0.05&\text{ }&0.10 \end{bmatrix}$

A risk is randomly selected in the portfolio and is observed for two calendar years. The observed results are: 2 claim in the first calendar year and 3 claims in the second calendar year.

Determine the Bayesian expected number of claims for the selected risk in year 3.

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.12$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.24$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.45$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.51$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.70$

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Problem 3-B

Using the same information as in Problem 3-A, determine the Buhlmann credibility estimate for the selected risk in year 3.

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.93$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.24$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.45$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.51$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.29$

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