CS2 Risk Modelling
Stochastic processes, Markov chains, and survival models: the risk mathematics behind insurance.
About CS2
CS2 applies advanced stochastic methods to insurance risk: survival analysis for mortality modelling, Markov chains for multi-state health insurance, credibility theory for experience rating, and extreme value theory for catastrophic events. Includes a compulsory R programming component from 2024 onwards.
Who is this for?
Students who have cleared or are nearly through CS1. Typically the fourth or fifth paper in most students’ progression. Essential for roles in life insurance, health insurance, and long-tail non-life lines.
155 days until CS2, April 2027
CS2A 16 Apr · CS2B 20 Apr · entry closes in 85 days
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Learn CS2 free — 8 worked explainers
One idea per page, explained from scratch, each ending in a worked example with the arithmetic shown in full. These are the ideas students most often get stuck on in CS2. Start anywhere.
- The survival function and the hazard rate, explained Move between the survival function, the density, the hazard rate and the integrated hazard, and compute a survival probability from any one of them
- The Kaplan-Meier estimator, and why censoring needs it Build a Kaplan-Meier survival table from censored data, compute the Nelson-Aalen estimate alongside it, and attach a standard error
- The Cox proportional hazards model, and what a hazard ratio means Read a fitted Cox coefficient as a hazard ratio, compute a survival probability from a baseline, and evaluate a partial likelihood
- Markov chains: transition matrices, Chapman-Kolmogorov and the stationary distribution Build a transition matrix, find multi-step probabilities with Chapman-Kolmogorov, and solve for a stationary distribution two independent ways
- Central exposed to risk, and the two mortality rates it produces Compute a central exposed to risk from a policy file and from a census, and turn it into both a force of mortality and a rate of mortality
- Bühlmann credibility: how much to trust one risk's own experience Estimate the two variances behind the credibility factor from a claims table and compute a credibility premium two ways
- Extreme value theory: block maxima, thresholds and the generalised Pareto distribution Fit a generalised Pareto distribution to threshold exceedances and use it to estimate a tail probability and a return level
- Copulas and Sklar's theorem: modelling dependence without touching the margins Separate marginal distributions from dependence using a copula, compute a joint tail probability and find a tail dependence coefficient
Every page is written by S.MONK and free to read. Nothing here asks for an email address.
Complete Syllabus
- Survival analysis: hazard function, Nelson-Aalen estimator, Kaplan-Meier, log-rank test
- Parametric survival models: exponential, Weibull, Gompertz, Cox proportional hazards
- Markov chains: transition matrices, Chapman-Kolmogorov equations, stationary distributions
- Multi-state models: disability income, long-term care, critical illness insurance
- Graduation methods: maximum likelihood, Bayesian, exposed-to-risk calculations
- Credibility theory: classical, Bühlmann, Bühlmann-Straub, Empirical Bayes
- Extreme value theory: block maxima, peaks-over-threshold, GPD distribution
- Copulas: Gaussian, t, Archimedean copulas, tail dependence, Sklar’s theorem
- R programming: survival analysis, GLMs, simulation in R (compulsory component)
Career Outcomes
Life Actuary, Health Actuary, Reserving Actuary, Pricing (long-tail non-life)
₹8–15 LPA with CM1+CS1+CS2 cleared
Do not neglect the R programming component. Past papers have specific R questions. S.MONK sessions include live coding demonstrations for every R section.
“CS2 has an R programming component that most students panic about. S.MONK spent time on the actual exam questions in R. I felt confident about the programming section, and most candidates did not.”