IFoA CM2 study guide
IFoA CM2 · Work through your exam, one topic at a time.
CM2, Actuarial Mathematics: Models, is one of the technical examinations in the Institute and Faculty of Actuaries' qualification pathway towards Fellowship. It sits after the earlier mathematical foundations subjects and is aimed at candidates who already handle calculus, probability and basic statistical inference and are ready to build and criticise full stochastic models. The IFoA CM2 study guide has 10 sections and about 3,771 words.
01Principles of Actuarial Modelling
This domain tests how you turn a messy real-world problem into a formal, testable representation, and how you judge whether the resulting model can be trusted. CM2 expects you to justify modelling choices, separate deterministic from stochastic approaches, and describe the control cycle linking data, assumptions, projection and monitoring.
355 words, about 2 min02The Binomial and Poisson Models
This domain covers the two workhorse models for counting events - deaths, claims, lapses, arrivals - and the assumptions that make each appropriate. X ~ Bin(n, p): n independent trials, constant p, two outcomes.
380 words, about 2 min03The Normal and Related Distributions
This domain tests the normal distribution, the sampling distributions derived from it, and the central limit theorem that justifies their widespread use in actuarial work. N(mu, sigma^2): symmetric, standardise with z = (x - mu)/sigma; roughly 68%, 95% and 99.7% of mass within 1, 2 and 3 standard deviations.
360 words, about 2 min04Estimators and Estimation
This domain asks how estimators are constructed from data and how they are judged - the criteria, the methods, and the asymptotic results that make large-sample inference possible. Bias: E[theta-hat] - theta.
381 words, about 2 min05Hypothesis Testing
This domain tests how to frame a question about a parameter as a choice between two models, and how to interpret the answer honestly. H0 versus H1; a test statistic; a critical region.
386 words, about 2 min06Linear Regression and Generalised Linear Models
This domain covers regression as a modelling framework, from ordinary least squares through to generalised linear models, which are the standard tool for mortality and claims rate modelling in actuarial practice. Y = X beta + epsilon with independent normal errors of constant variance.
361 words, about 2 min07Time Series and Stochastic Processes
This domain covers models for data observed in sequence, where dependence between successive observations is the whole point rather than an inconvenience. Weak stationarity means constant mean and variance, with autocovariance depending only on the lag.
356 words, about 2 min08Markov Chains and Markov Jump Processes
This domain covers state-based models of movement between conditions - healthy, sick, dead; or claim-free, one claim, two claims - in both discrete and continuous time. The Markov property: the future depends on the past only through the present state.
400 words, about 2 min09Survival Models and Life Table Estimation
This domain covers the modelling of time to an event when observation may be incomplete, and the construction of survival and mortality estimates from data. S(t) = P(T t); density f(t); hazard mu(t) = f(t)/S(t); cumulative hazard H(t) = integral of mu = -log S(t), so S(t) = exp(-H(t)).
389 words, about 2 min10Graduation and Mortality Projection
This domain covers turning noisy crude mortality rates into a smooth, usable mortality table, and then projecting that table forward in time. Crude rates are erratic, especially at old ages where exposure is thin.
403 words, about 2 min