Ruin Probability Estimate Calculator

Work out ruin probability estimate instantly with clear inputs, formula shown and shareable results.

About Ruin Probability Estimate Calculator

Classical risk theory with exponential claim sizes gives an exact ruin probability: ψ(u) = e^(−Ru)/(1 + θ), where the adjustment coefficient R = θ/((1+θ)μ). Ruin risk falls exponentially in surplus and in the safety loading built into premiums.

Formula

Cramér-Lundberg (exponential claims)

ψ(u) = 1/(1+θ) · e^(-Ru); R = θ/((1+θ)μ)

u: Surplus
θ: Safety loading
μ: Mean claim

Worked example

With the default values below, Ruin Probability Estimate Calculator returns Probability Of Ultimate Ruin of 6.40265%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Initial Surplusminimum 0: 500,000
Mean Claim Sizeminimum 0: 25,000
Premium Safety Loadingaccepts 0.1–200 %: 15 %

Results

Probability Of Ultimate Ruin: 6.40265%
Adjustment Coefficient (per million): 5.2174
Survival Probability: 93.59735%
Surplus Needed For 1% Ruin: $855,869.91

Step by step

1Values used
2Cramér-Lundberg (exponential claims)
3Probability Of Ultimate Ruin= 6.40265
4Adjustment Coefficient (per million)= 5.2174
5Survival Probability= 93.59735
6Surplus Needed For 1% Ruin= 855,869.91

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax or compounding frequency into account.
Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What does the safety loading mean?

It is the margin premiums carry above expected claims. With no loading ruin is certain, however large the surplus.

Is this a realistic model?

It is a benchmark. Real books have heavier-tailed claims, reinsurance and dividends, all of which need simulation.