Perform calculations for sums of compound Poisson models.

Free SOA Exam ASTAM (Advanced Short-Term Actuarial Mathematics) lesson in Aggregate Models. 27 min read, ~3,997 words.

If are independent, then is with and. The combined severity is a mixture with mixing weights (proportional to frequency), not a convolution. and use the second raw moment and bypass the mixture entirely. MGF factorizes:, so exponents add and total rate is. A single compound Poisson with mixture severity decomposes...