Annual aggregate loss
runAggregateLoss — compound negative-binomial with lognormal severity
Mean
$21.70m
Std dev
$9.54m
CV
0.440
Claim-free year
0.00%
Value at risk, and beyond it
| Percentile | VaR | TVaR | TVaR − VaR |
|---|---|---|---|
| 50.0% | $20.27m | $28.97m | $8.70m |
| 90.0% | $33.92m | $41.37m | $7.45m |
| 99.0% | $50.83m | $58.22m | $7.39m |
| 99.5% | $55.24m | $63.75m | $8.51m |
TVaR is the mean of the losses BEYOND the percentile, so it is always above VaR. The gap is what a VaR-only capital number declines to look at.
The distribution checks itself
The compound mean and standard deviation have closed forms — E[N]·E[X] and √(E[N]·Var[X] + Var[N]·E[X]²) — computed without simulating anything. The engine returns them alongside the empirical figures so the two can be compared, which is the only cheap way to catch a distribution that has quietly gone wrong.
Mean drift
0.45%
vs closed form
SD drift
0.14%
vs closed form
Why it matters
20,000 trials at seed 424242. The same seed reproduces this distribution exactly; switch to Panjer and the answer comes from a completely different route. Agreement between them is evidence — a single method agreeing with itself is not.
Stated limit
Frequency and severity are assumed independent, which is the collective risk model's own assumption rather than the platform's claim about your book. A year where big losses also arrive more often is a different model, and this one will understate its tail.