Work out aggregate loss distribution instantly with clear inputs, formula shown and shareable results.
For a compound Poisson model the aggregate loss has mean λμ and variance λ(σ² + μ²), so both claim count and claim size volatility feed the spread. A normal approximation then gives a working 95th percentile for capital setting.
Compound Poisson moments
E[S] = λμ; Var[S] = λ(σ² + μ²); VaR₉₅ ≈ E[S] + 1.645·SD[S]
The variance term carries both σ² and μ², because random claim counts alone already create spread even with fixed severities.
Only for large, well-diversified portfolios. Skewed books need translated gamma, Panjer recursion or simulation.