**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.

The following provides more information about the risks in Class 1:

- 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.

The following provides more information about the risks in Class 2:

- 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).

___________________________________________________________________________________

**Problem 12-A**

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

___________________________________________________________________________________

**Problem 12-B**

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

___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

### Like this:

Like Loading...

*Related*

Tagged: Actuarial Exam, Buhlmann Credibility, CAS Exam 4, CAS Exam 4 Practice Problem, Frequency, Loss Models, Poisson Distribution, Poisson-Gamma Model, Probability, Pure Premium, SOA Exam C, SOA Exam C Practice Problem

## Leave a Reply