Use convolution and recursive formulas to derive probability and distribution functions for aggregate claims distributions with (a,b,0) or (a,b,1) frequency, and with discrete severity distributions.
Free SOA Exam ASTAM (Advanced Short-Term Actuarial Mathematics) lesson in Aggregate Models. 28 min read, ~4,223 words.
Aggregate pmf via conditioning:. (a,b,0) class: ratio for. Members: Poisson, binomial, negative binomial. (a,b,1) class: same ratio for; and free. Includes zero-truncated and zero-modified versions. Panjer (a,b,0), severity on positives:,. (a,b,1) Panjer adds a correction to absorb the modified first two probabilities. Severity zero mass: when, start at and divide...
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What this lesson covers
- Content
- Example 1
- Example 2
- Example 3
- Example 4
- Example 5
- Example 6
- Common Mistakes
- Key Takeaways
- Exam Shortcuts
Learning objectives
- 2a
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