SOA Exam ASTAM Sample Question 4
Study guide: Exam ASTAM
CBA Insurance Company splits drivers into three categories – Safe, Not So Safe, and Reckless. Within each category, claim frequency is Poisson distributed, and claim severity is Gamma distributed, but the parameters of the frequency and severity distributions differ, as shown in the following table.
| Type | Proportion of Total Drivers | Frequency parameter | Severity parameters |
|---|---|---|---|
| Safe | 0.5 | \lambda=0.04 |
\alpha = 3, \theta = 1000 |
| Not So Safe | 0.3 | \lambda=0.10 |
\alpha = 4, \theta = 1000 |
| Reckless | 0.2 | \lambda=0.25 |
\alpha = 5, \theta = 1000 |
Part a
The expected value of the process variance of the claim severities (for the observation of a single claim) under automobile coverage is 4 million to the nearest million. Calculate it to the nearest 1000.
Part b
What is the variance of the hypothetical means for claim severities (for the observation of a single claim) under automobile coverage?
Part c
Over several years, an individual driver with automobile coverage has single claim of 20,000. Use Bühlmann Credibility to estimate this driver's future average claim severity.
Part d
What is the expected value of the process variance of the pure premium (for the observation of a single exposure) under this coverage?
Answer this question and see the worked solution
Concepts tested
- Bühlmann Credibility
- Credibility
- Expected Value of Process Variance
- Variance of Hypothetical Means
- Aggregate Loss Model