Actuarial Notes

SOA Exam ASTAM Sample Question 1

Study guide: Exam ASTAM

Santiago Substandard Auto Company (SSAC) sells automobile insurance to drivers with bad driving records. Each policy only covers one automobile.

During 2021, SSAC had 10,000 policies. There were no deductibles, no upper limit, and no coinsurance, so that each policy covered 100% of all losses.

During 2021, the number of claims per insured automobile for SSAC was:

Number of claims in 2021 Number of Policies
0 2400
1 3400
2 2400
3 1500
4 300

Part a

First, assume that the claim frequency is distributed as a Poisson random variable with mean parameter \lambda. Calculate the 90% linear confidence interval for \lambda based on the above data.

Part b

Using the Chi-Square Test with a 99% significance level, SSAC wishes to use the data to test the following hypotheses:

  • H_0: The data is from a Poisson distribution.
  • H_1: The data is not from a Poisson distribution.

The data for 3 and 4 claims in 2021 are combined for this test.

  • (i) Calculate the Chi-Square test statistic.
  • (ii) Calculate the p-value for this test and state your conclusion with regard to the hypotheses.

Part c

You are given the following claim severity sample from 2021:

200 1000 5000 10,000 100,000

Using the Kolmogorov-Smirnov Test with a 95% significance level, SSAC uses this data to test the following hypotheses:

  • H_0: The data is from a Pareto distribution with \alpha = 4 and \theta = 75{,}000.

  • H_1: The data is not from a Pareto distribution with \alpha = 4 and \theta = 75{,}000.

  • (i) Calculate the Kolmogorov-Smirnov Test statistic.

  • (ii) You are given that the 5% critical value for the Kolmogorov-Smirnov test is approximately \dfrac{1.36}{\sqrt{n}}.

    State your conclusion.

Part d

In selecting a model, there are two important concepts. The first concept is known as parsimony while the second concept does not have a specific name.

  • (i) State the principle of parsimony.
  • (ii) State the second concept.
  • (iii) Identify the score-based approach that is consistent with parsimony and state why it is consistent.

Answer this question and see the worked solution

Concepts tested

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