The Library

The vocabulary every actuary must speak fluently: exposure, premium, loss, LAE, IBNR/IBNER, and the accident/policy/report/calendar year conventions.

Force of interest, annuities-certain, and duration — the time-value machinery behind discounted reserves, investment income, and Exam FM/2.

A brief, P&C-actuary-oriented tour of survival models, life tables, and the present values of life insurance and annuities.

The frequency and severity distribution families actuaries use every day, their moments and MGFs, and how mixtures build realistic loss models.

MLE and method of moments, Bayesian estimation, the difference between confidence and credible intervals, and hypothesis testing as actuaries actually use it.

Full-credibility derivation and the square-root rule, Bühlmann and Bühlmann–Straub with a worked three-group example, Bayesian Poisson–Gamma, and complement of credibility.

Increased limits factors, the ILF curve, umbrella/excess exposure vs. experience rating, and territory and class relativities, with a worked ILF example.

Tweedie GLMs with log links and offsets for pure premium modeling, relativity extraction, lift/Gini validation, GBM comparisons, interpretability, and ASOP 56 model governance.

The fundamental insurance equation, loss ratio and pure premium indication methods, on-leveling via the parallelogram method, trending, and development.

Payroll exposure, NCCI loss costs and LCMs, class relativities, benefit-level and law-amendment factors, and a fully worked experience rating (mod) calculation.

How loss triangles are built, age-to-age (ATA) factor calculation and averaging methods, judgmental selection, and tail factor methods, with a worked 4x4 example.

Point estimates versus reasonable ranges, disclosure requirements under ASOP 43, and how to size a reserve range using method dispersion and the Mack CV.

Paid/incurred diagnostic ratios, closure rate and average case reserve monitoring, and the Berquist-Sherman case-reserve-adequacy and settlement-rate adjustments, with a small worked example.

Formulas and appropriate use cases for the chain ladder, expected-claims, Bornhuetter–Ferguson, Benktander, and Cape Cod methods, with a worked comparison on one origin year.

Mack's three chain-ladder assumptions, the full mean squared error of prediction formula with each term explained, sigma_k estimation, the ODP bootstrap algorithm, and derivation of percentiles and risk margins.

Building premium bridges and rate-vs-trend roll-forwards, decomposing the combined ratio, expressing forecasts as scenario ranges, and constructing driver-based plans.

Statutory vs. GAAP accounting for P&C insurers, the structure of Schedule P and IRIS ratios, an overview of the RBC formula, and a worked one-year reserve-development example.

Compound distribution theory for aggregate losses: moments, the Panjer recursion, FFT and simulation approaches, and applications to aggregate deductibles and stop-loss pricing.

Sklar's theorem and the major copula families, Kendall's tau relationships, tail dependence, simulation, and how to stress-test dependence assumptions in a capital model.

Fisher–Tippett and the GEV family, the peaks-over-threshold/GPD approach, mean-excess plots, the Hill estimator, and how heavy tails drive reinsurance layer pricing.

A tour of proportional and non-proportional reinsurance structures, ceding commissions and reinstatements, and the experience- and exposure-rating methods used to price them.

VaR and TVaR, the coherence axioms and VaR's subadditivity failure, distortion and spectral risk measures, Euler capital allocation, and an overview of RBC, Solvency II SCR, and ORSA.

Scenario design and reverse stress testing, and a survey of emerging risks — medical and social inflation, legislative change, recessionary WC frequency effects, cyber, and pandemic — with a worked medical-inflation reserve shock.

ASOP 41 disclosure requirements, structuring a BLUF actuarial memo, tailoring communication to underwriting, claims, and finance audiences, and a peer review checklist.

ASOP 23's requirements for reviewing and relying on data, practical reconciliation and control-total checks, and how to document data limitations in an actuarial work product.

Building loss development triangles from raw claim transactions in SQL, fitting chain-ladder and Mack models in Python and R, and reproducibility practices for actuarial code.

How the CAS exam sequence, SOA equivalents, and CPCU designation fit together, with syllabus themes, study strategy, spaced repetition, and how Actuarium's sections map to each exam.