Aggregate loss simulator

Monte Carlo simulation of Poisson or negative binomial claim counts with lognormal, Pareto or exponential severities, gross and net of per-risk excess of loss reinsurance, with VaR, TVaR and an exceedance curve.

Inputs

Expected number of claimsVariance of the numberClaim severityMean claimCoefficient of variation%Per-risk excess of lossXoL retentionXoL limitConfidence%Simulated yearsRandom seed

Results

Mean gross loss

2,396,550.97

Exact 2,400,000.00

Standard deviation

514,921.77

Exact 513,809.30

Gross VaR 99.5%

4,151,035.28

TVaR 4,639,273.63

Net VaR 99.5%

3,105,509.86

Net mean 2,112,432.10, TVaR 3,445,258.99

Annual loss by return period

GrossNet

Explain this result

Get a plain-English reading of the numbers above and what drives them.

Preview: rule-based reading. AI-assisted explanations run on the analytics core.

Exceedance table

Return period	Probability	Gross	Net
1 in 2	50.0%	2,342,700.79	2,095,926.97
1 in 5	20.0%	2,782,456.66	2,391,944.32
1 in 10	10.0%	3,048,611.25	2,554,877.73
1 in 20	5.0%	3,301,385.08	2,698,432.60
1 in 50	2.0%	3,636,192.82	2,873,809.89
1 in 100	1.0%	3,870,216.66	2,987,277.70
1 in 200	0.5%	4,151,035.28	3,105,509.86
1 in 500	0.2%	4,522,172.78	3,287,584.83

Methodology

Conventions

Claim counts are Poisson when the variance equals the mean, otherwise negative binomial (a Poisson whose mean is gamma-distributed). Severities are independent of each other and of the count.
Per-risk excess of loss cedes min(max(X − R, 0), L) of each claim. The seed fixes the random numbers, so a run can be repeated.
VaR is the chosen percentile of the annual total, and TVaR the average of the totals beyond it.

References

Klugman, Panjer and Willmot, Loss Models: From Data to Decisions, 5th ed.

Formulas

Aggregate loss: S = X_1 + \dots + X_N
Mean: E[S] = E[N]\,E[X]
Variance: \operatorname{Var}(S) = E[N]\operatorname{Var}(X) + \operatorname{Var}(N)\,E[X]^2