Actuarial science bibliography

An open, interactive textbook covering frequency and severity modelling, aggregate loss models, loss reserving, credibility, premium principles, dependence and copulas, simulation and portfolio management, with R code and exercises.

The CAS Exam 5 ratemaking text: exposures, premium, losses and LAE, trending, development, overall indication (pure premium and loss ratio methods), classification ratemaking, GLMs, credibility, territory and increased-limit factors, and implementation.

The CAS Exam 5 reserving text: claims data organisation, development triangles, the development (chain ladder), expected claims, Bornhuetter-Ferguson, Cape Cod, frequency-severity and case-outstanding techniques, tail factors, ULAE and reserve evaluation.

The original paper introducing the Bornhuetter-Ferguson method, which blends an a priori expected loss ratio with reported development to estimate IBNR, and discusses its use for reinsurance and immature accident years.

Mack's distribution-free chain ladder model: the three assumptions, unbiased development factors, the formula for the mean squared error of reserve estimates, and diagnostic tests for calendar-year effects and development-factor independence.

Open-access monograph on exponential dispersion families, GLMs, credibility, regularisation, neural networks, deep learning for claims frequency and severity, model validation, interpretability and telematics, with actuarial examples throughout.

Introduces the distribution-free chain ladder model and an analytic formula for the standard error (mean squared error of prediction) of chain ladder reserve estimates, separating process and estimation variance.

The founding paper of greatest-accuracy (Bühlmann) credibility: the linear Bayes estimator Z x̄ + (1 − Z) μ with Z = n/(n + k), k = EPV/VHM, derived by minimising expected squared error.

A comprehensive survey of stochastic reserving: over-dispersed Poisson and negative binomial GLMs, Mack's model, log-normal models, bootstrapping and Bayesian methods, with prediction errors and worked examples.

Generalises gamma-cell reserving models to Tweedie's compound Poisson family within a GLM, estimating the power parameter and producing reserve estimates and their variability.

Revisits Mack's and Murphy's MSEP estimates through a time-series formulation of the chain ladder method, deriving a conditional MSEP that differs subtly from Mack's formula.

Defines the axioms of coherent risk measures — monotonicity, subadditivity, positive homogeneity and translation invariance — shows VaR fails subadditivity, and characterises coherent measures via scenario sets.

Proposes the CBD two-factor stochastic mortality model for older ages, calibrates it to England & Wales data and shows how parameter uncertainty affects longevity risk pricing.

The Lee–Carter model: log m(x,t) = a(x) + b(x) k(t) + ε, fitted by SVD with k(t) forecast as a random walk with drift, giving probabilistic mortality and life-expectancy forecasts.

A free manuscript covering chain ladder, Bornhuetter–Ferguson, Bayesian and credibility reserving, claims development results for solvency, and the one-year view under Solvency II.

Benchmarks GLMs, regression trees, boosting and neural networks for claims-frequency modelling on the freMTPL2 dataset, with reproducible code and a discussion of model comparison.