CS2 Risk Modelling & Survival Analysis
Markov chains, survival estimation, time series, reserving triangles, ruin and copulas, with the CS2 formula sheet and the CS1 statistics it assumes.
Interactive tools
Statistical tables
Normal, Student's t, chi-squared and F: the classic printed tables plus exact calculators and shape plots for any parameters, inverse percentiles and two-sided critical values. Handy for CS1, CS2 and any stats exam.
Ruin theory simulator
Compound Poisson claims against premium income: ruined paths highlighted, simulated ruin rates against the exact Cramér-Lundberg formula. CS2.
Survival models playground
Gompertz-Makeham mortality with live sliders: survival curves, force of mortality and life expectancy. Illustrative law, not a published table. CS2 and CM1.
Run-off triangles
Edit a cumulative claims triangle and watch the chain ladder complete it, with expected loss ratio and Bornhuetter-Ferguson reserves side by side — plus every formula, an Excel walk-through and a test-yourself mode with worked solutions. CS2 reserving.
No-claims discount simulator
The CS2 Markov chain classic: transition matrix, year-by-year convergence and the stationary distribution, with the long-run average premium in pounds. Includes a test-yourself mode with worked solutions.
Time series playground
Simulate AR, MA and ARMA processes and watch the sample ACF and PACF against theory: cut-offs, tailing-off and the slow decay of near-unit roots. CS2.
Multi-state model simulator
The healthy-sick-dead illness-death model: move the transition intensities, watch the occupancy probabilities evolve, and see the sickness benefit premium price itself. CS2.
Kaplan-Meier playground
Edit a survival dataset with censoring toggles and watch the product-limit estimate, the Nelson-Aalen overlay and the full risk-set table rebuild live. CS2, with a test-yourself mode and worked solutions.
Copula visualiser
Gaussian, t, Clayton and Gumbel scatter clouds at the same Kendall's tau: watch tail dependence appear in the corners while the correlation stays fixed. CS2.
Extreme value theory
The GEV density morphing through Fréchet, Gumbel and Weibull on a shape slider, plus a peaks-over-threshold mean excess plot on simulated Pareto and exponential claims. CS2.
Reinsurance layers
A claim severity density split at the retention: insurer and reinsurer expected costs, shares and the variance relief, recomputed live as you slide M. Excess of loss for CS2.
Value at Risk & Expected Shortfall
Slide the confidence level and watch VaR and TVaR move on Normal and fat-tailed t distributions, run a historical simulation on a dealt year of daily P&L, and see the two-loans example where VaR fails subadditivity. CS2, CM2 and SP5, with a test-yourself mode and worked solutions.
Reference sheets
Probability distributions cheat sheet
Every CS1 distribution on one page: what it models, density, mean, variance and generating function, from Bernoulli to the F distribution. Assumed knowledge for CS2.
CS2 formula cheat sheet
Survival analysis, mortality laws, Markov processes, time series, loss distributions, EVT, ruin and copulas: the formulas CS2 keeps coming back to, rendered properly on one page.
CS1 formula cheat sheet
Distribution moments, the CLT and sampling distributions, maximum likelihood and the Cramér-Rao bound, regression, Bayesian methods, credibility and GLMs: the CS1 core rendered properly on one page. CS2 assumes all of it.