Ruin theory simulator
An insurer's surplus as a race between steady premium income and randomly arriving claims. Watch paths that dip below zero get marked as ruined, and compare the simulated ruin rate with the exact formula.
Claims arrive as a Poisson process at rate λ with Exponential(1) sizes; premiums come in continuously at (1+θ)λ. For exponential claims the infinite-horizon ruin probability has the closed form ψ(u) = e^(−Ru)/(1+θ) with adjustment coefficient R = θ/(1+θ) — the simulation sits a little below it because paths only run for 10 years. Notice surplus and loading fight ruin exponentially, while λ mostly just speeds the clock up.
What the sliders teach
Capital and loading are the two levers that matter: the ruin probability falls exponentially in the initial surplus u (each extra unit of capital multiplies safety) and the adjustment coefficient R grows with the loading θ. The claim rate λ barely changes the destination — it mostly changes how fast you get there, which is why the infinite-horizon formula has no λ in it. This is CS2's Cramér-Lundberg model with exponential claims, the one case with a clean closed form.
Make it stick. Studying CS2? Memori's shop carries a ready-made risk-modelling set, and the notation cheat sheet covers the symbols. Memori is a flashcard app built by actuarial students — join the beta.
For education only, not financial advice.