Work out ruin probability estimate instantly with clear inputs, formula shown and shareable results.
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.
Cramér-Lundberg (exponential claims)
ψ(u) = 1/(1+θ) · e^(-Ru); R = θ/((1+θ)μ)
It is the margin premiums carry above expected claims. With no loading ruin is certain, however large the surplus.
It is a benchmark. Real books have heavier-tailed claims, reinsurance and dividends, all of which need simulation.