ASTAM: Compound totals reveal which variance assumption you used
The variability of a total comes from severity and frequency. Write the conditional expectation and variance first; then use total expectation and total variance. This makes the assumptions visible and helps avoid mixing compound Poisson and fixed-count results.
Worked example or practice scenario
A Poisson count with mean 4 and independent exponential severities with mean 200 gives E[S]=800. Severity second moment is 80,000, so Var(S)=4×80,000=320,000. The standard deviation is about 565.69.
Try this next
Compare with exactly four severities: the variance would be 160,000. Now consider a negative-binomial frequency with variance larger than its mean. Explain which term grows before using any numerical approximation.
Reading sources
ActNet editorial guide · October 1, 2026 · Original illustrative examples.
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