Essential library

Landmark books of actuarial science worldwide

From the foundations of the 18th century to modern reference texts: the works that defined actuarial science and trained generations of actuaries.

Actuarial science was built one book at a time. Behind every life policy, every reserve and every pension model lies an intellectual tradition that begins with Jacob Bernoulli's probability and reaches stochastic reserving methods and data science. This is a selection of the profession's most iconic works worldwide (foundational classics, exam texts and research references), with their cover, authorship and why they remain required reading.

The foundations (18th and 19th centuries)

The works that founded probability and the mathematics of life insurance.

Cover of Ars Conjectandi
Ars Conjectandi
J. Bernoulli
Ars Conjectandi
Jacob Bernoulli
1713 · Basel

The work that founded probability theory and proved the law of large numbers. It is the mathematical root of all actuarial science: without it there would be no measurement of risk.

Cover of Observations on Reversionary Payments
Observations on Reversionary Payments
R. Price
Observations on Reversionary Payments
Richard Price
1771 · London

It laid the mathematical foundations of life insurance and pensions. It gave rise to the "Northampton tables," which governed pricing in the British market for decades.

The classics of actuarial theory

Life, non-life, risk and credibility: the backbone of actuarial education.

Cover of Actuarial Mathematics
Actuarial Mathematics
Bowers et al.
Actuarial Mathematics
Bowers, Gerber, Hickman, Jones & Nesbitt
1986 / 1997 · Society of Actuaries

"The bible" of life actuarial mathematics. It trained generations of actuaries and was for decades the core text for the SOA exams.

Cover of Actuarial Mathematics for Life Contingent Risks
Actuarial Mathematics for Life Contingent Risks
Dickson, Hardy & Waters
Actuarial Mathematics for Life Contingent Risks
Dickson, Hardy & Waters
2009 / 2020 · Cambridge University Press

The modern successor to Bowers. The official text for the SOA and IFoA life exams, with an emphasis on cash flows and multiple state models.

Cover of Loss Models
Loss Models: From Data to Decisions
Klugman, Panjer & Willmot
Loss Models: From Data to Decisions
Klugman, Panjer & Willmot
1998 · Wiley

The worldwide reference on loss models for property and casualty insurance. The basis of the SOA short-term actuarial modeling exams (STAM/short-term).

Cover of Life Insurance Mathematics
Life Insurance Mathematics
H. U. Gerber
Life Insurance Mathematics
Hans U. Gerber
1986 · Springer / Swiss Re

An elegant and concise treatment of life insurance mathematics. A European classic valued for its rigor and clarity.

Cover of Non-Life Insurance Mathematics
Non-Life Insurance Mathematics
T. Mikosch
Non-Life Insurance Mathematics
Thomas Mikosch
2004 · Springer

A rigorous reference on non-life insurance: counting processes, ruin theory and aggregate claims models.

Cover of Mathematical Methods in Risk Theory
Mathematical Methods in Risk Theory
H. Bühlmann
Mathematical Methods in Risk Theory
Hans Bühlmann
1970 · Springer

A foundational work of risk theory and credibility theory. "Bühlmann credibility" is required reading in pricing.

Cover of Practical Risk Theory for Actuaries
Practical Risk Theory for Actuaries
Daykin, Pentikäinen & Pesonen
Practical Risk Theory for Actuaries
Daykin, Pentikäinen & Pesonen
1994 · Chapman & Hall

The bridge between risk theory and practice: solvency and capital models that anticipated the Solvency II framework.

Advertisement

From compound interest to data science

Modern actuarial science rests on financial mathematics, stochastic processes and, increasingly, statistics and machine learning. These texts are classic bridges into those fields.

Cover of The Theory of Interest
The Theory of Interest
S. Kellison
The Theory of Interest
Stephen G. Kellison
1970 · Irwin / McGraw-Hill

The classic of financial mathematics. The go-to text for the SOA financial mathematics (FM) exam for decades.

Cover of Mathematics of Investment and Credit
Mathematics of Investment and Credit
S. Broverman
Mathematics of Investment and Credit
Samuel A. Broverman
1991 · ACTEX

A standard for the SOA FM exam: theory of interest, bond valuation and analysis of financial instruments, with a practical focus.

Cover of Options, Futures, and Other Derivatives
Options, Futures, and Other Derivatives
J. C. Hull
Options, Futures, and Other Derivatives
John C. Hull
1988 · Prentice Hall

The global reference on financial derivatives. An indispensable bridge between actuarial science and quantitative finance.

Cover of Derivatives Markets
Derivatives Markets
R. McDonald
Derivatives Markets
Robert L. McDonald
2002 · Addison-Wesley / Pearson

The financial economics text for the SOA IFM/MFE exams. Option valuation and pricing models for actuaries.

Cover of Introduction to Probability Models
Introduction to Probability Models
S. Ross
Introduction to Probability Models
Sheldon M. Ross
1972 · Academic Press

A universal classic on stochastic processes and Markov chains. The probabilistic foundation on which actuarial modeling is built.

Cover of Regression Modeling with Actuarial and Financial Applications
Regression Modeling with Actuarial and Financial Applications
E. Frees
Regression Modeling with Actuarial and Financial Applications
Edward W. Frees
2009 · Cambridge University Press

A bridge between regression statistics and actuarial applications. A forerunner of the profession's turn toward data science.

Cover of Stochastic Claims Reserving Methods in Insurance
Stochastic Claims Reserving Methods in Insurance
Wüthrich & Merz
Stochastic Claims Reserving Methods in Insurance
Mario V. Wüthrich & Michael Merz
2008 · Wiley

The modern reference on stochastic reserving (chain ladder, Mack, bootstrap). Essential for reserve valuation and Solvency II.

Specialties: property and casualty, pensions and data science

References by field, aligned with the CAS (property and casualty insurance), AMAC (pensions) and the new wave of predictive analytics.

Foundations of Casualty Actuarial Science
CAS
Foundations of Casualty Actuarial Science
Casualty Actuarial Society (multiple authors)
4th ed., 2001 · CAS

"The bible" of property and casualty insurance. The Casualty Actuarial Society's reference text: pricing, reserving and risk theory for property and casualty.

Introduction to Ratemaking and Loss Reserving
Brown & Lennox
Introduction to Ratemaking and Loss Reserving for Property and Casualty Insurance
Robert L. Brown & W. Scott Lennox
2015 · ACTEX

A practical entry point to ratemaking and loss reserving in property and casualty insurance. Core reading for the CAS exams.

Modern Actuarial Risk Theory
Kaas et al.
Modern Actuarial Risk Theory
Kaas, Goovaerts, Dhaene & Denuit
2nd ed., 2008 · Springer

A modern reference on risk theory: aggregate loss models, credibility, GLMs and ruin theory. Widely used in Europe and in graduate programs.

Generalized Linear Models for Insurance Data
de Jong & Heller
Generalized Linear Models for Insurance Data
Piet de Jong & Gillian Z. Heller
2008 · Cambridge University Press

The text that brought generalized linear models (GLMs) to the heart of insurance pricing. The foundation of actuarial predictive analytics.

Pension Mathematics
H. Winklevoss
Pension Mathematics with Numerical Illustrations
Howard E. Winklevoss
2nd ed., 1993 · Pension Research Council / Wharton

A classic of pension mathematics: costing, liabilities and funding of defined benefit plans, with numerical examples.

Fundamentals of Private Pensions
McGill et al.
Fundamentals of Private Pensions
McGill, Brown, Haley, Schieber & Warshawsky
9th ed., 2010 · Oxford University Press

The reference work on the design, regulation and funding of private pension plans. Essential for the retirement actuary.

Predictive Modeling Applications in Actuarial Science
Frees et al.
Predictive Modeling Applications in Actuarial Science
Edward W. Frees, Richard A. Derrig & Glenn Meyers
2014 · Cambridge University Press

Two volumes that consolidate the profession's turn toward data science: GLMs, trees, Bayesian credibility and predictive models applied to insurance.

An Introduction to Statistical Learning
James et al.
An Introduction to Statistical Learning
James, Witten, Hastie & Tibshirani
2013 · Springer

The most popular entry point to machine learning. Regression, classification, resampling and trees: tools that are now indispensable for the actuary and data scientist.

Ruin Probabilities
Asmussen & Albrecher
Ruin Probabilities
Søren Asmussen & Hansjörg Albrecher
2nd ed., 2010 · World Scientific

The modern treatise on ruin theory: probability of insolvency, risk processes and heavy tails. A reference for solvency and capital.

Introduction to Credibility Theory
T. Herzog
Introduction to Credibility Theory
Thomas N. Herzog
4th ed., 2010 · ACTEX

A clear, teaching-oriented text on classical, Bühlmann and Bayesian credibility: how to combine your own experience with market experience for pricing.

How to use this list

It is not a ranking but a map. The foundations explain where the profession comes from; the theory classics remain the basis of the exams of associations such as the SOA, CAS and IFoA; and the finance and data texts point to where it is heading. For Mexican students, many of these titles appear in the reading lists of UNAM, ITAM, Anáhuac and the other actuarial science degree programs.

Covers courtesy of Open Library (openlibrary.org). The images correspond to specific editions cataloged in that open collection and may differ from the most recent edition of each work. Trademarks and covers are the property of their respective publishers; they are shown for informational and bibliographic reference purposes.