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. 30 min read, ~4,453 words.

Aggregate pmf by conditioning on count:; the pgf identity yields and the compound variance. (a,b,0) class: ratio for, exactly Poisson, binomial, and negative binomial, identified by the sign of. (a,b,1) class: same ratio for with and free; includes zero-truncated and zero-modified versions. Panjer (a,b,0), severity on positives:,. (a,b,1) Panjer adds...

What this lesson covers

• Content
• Example 1
• Example 2
• Example 3
• Example 4
• Example 5
• Example 6
• Common Mistakes
• Check Your Understanding
• Exam Shortcuts

Learning objectives

• 2a

Browse all free Exam ASTAM lessons or jump into free Exam ASTAM practice questions.