The History of Actuarial Science

When I began researching the history of actuarial science, I anticipated reading about a couple centuries of actuarial history. However, I soon realized that the concepts underlying the actuarial profession go back not just centuries, but thousands of years.

I was not expecting the origins of risk management and probability theory to involve a French gambler, a London coffeehouse, a famous astronomer or ancient Roman courts. But that is what I found, and much more.

In this article, I will first deconstruct the history of actuarial science into building blocks to understand how the profession got to where it is today. Then I will trace the development of the profession back to medieval times when actuarial science became formally recognized. Finally, I will extract lessons—some of them surprising—to imagine how the actuarial profession may continue to evolve.

Ancient Roots of Insurance Principles

Nearly 4,000 years ago, in 1750 B.C., the Code of Hammurabi in ancient Babylon reflected early attempts to quantify risk and compensation for losses. One of the oldest known legal codes, it discussed a form of bottomry, or loan repayment contingent on a successful voyage.¹

There also are records of early methods of insurance-like protection arising from charity, such as mutual aid-friendly societies in ancient Greece and Rome.^2,3,4 Members contributed fees in exchange for support during illness, disability or death. Nonlife insurance possibly started as a hedge against loss of cargo during sea travel, as mentioned in anecdotal reports in the writings of Greek orator Demosthenes as early as the fourth century B.C.⁵

In terms of the origins of financial accounting, early forms of recordkeeping in Mesopotamia involved clay tablets dating between 2500 B.C. and 50 B.C. that contained details about transactions involving animals and commodities.⁶ Ancient accounting practices also developed in other civilizations, such as in Egypt.⁷

Development of Probability Theory in Medieval Times

There are several theories as to why the study of probability theory was not popular before the mid-17^th century. These include an absence of economic motivation and a religious worldview where some writers claimed, “God directly determines the outcome of all randomized events both in divination and in gambling,” a view English theologian Thomas Gataker questioned in 1619.⁸

In 1654, French writer and philosopher Antoine Gombaud, also known as Chevalier de Mere, became a prominent adviser in the court of Louis XIV.⁹ But he also had another passion: gambling.¹⁰ Throughout his time at the gaming tables, he ran into mathematical problems that required the help of his friend, mathematician Blaise Pascal.¹¹ One key question was the division problem: If a game of chance is interrupted midway, where both sides had an equal chance of winning each round, how should the winnings be divided among the players?

While the Italian polymath Gerolamo Cardano had worked on analyzing games of chance in the 16^th century,¹² Pascal’s solution to the division problem was a decisive breakthrough. What started out as a question about a game turned into a fierce mathematical debate in a series of letters between young Pascal and the renowned mathematician Pierre de Fermat. This unlikely correspondence laid the foundation for probability theory.

Probability theory continued to develop during the 18^th century with the work of English statistician and philosopher Thomas Bayes, who never actually published the result for which he is remembered—Bayes’ Theorem. Bayes’ work on probability theory was published after his death and contained multiple amendments and additions from his friend Richard Price.¹³

The Beginnings of Insurance

Marine insurance contracts resembling the modern insurance concept first appeared in Genoa and Florence, Italy, around the mid-14^th century.¹⁴ In Genoa, insurance contracts were initially disguised as a way to avoid charges of usury (lending money at unreasonably high interest rates).

The earliest known life insurance policy was taken out on the life of a London citizen, William Gibbons, in 1583 for a term of 12 months. His death nearly a year later led to a legal dispute on whether or not the sum assured should be paid, as he had lived for 12 months if a month had 28 days but not for 12 full calendar months.¹⁵ Several cities in Europe began to publish mortality tables on a weekly basis throughout the 16^th and 17^th centuries.¹⁶

By the 17^th century, it was commonplace to insure ships and cargoes at the Royal Exchange in London¹⁷ and for business to occur in coffeehouses.¹⁸ One notable example was Edward Lloyd’s coffeehouse by the river Thames in London, which laid the foundation for the Lloyd’s of London insurance market.¹⁹

The Creation of Actuarial Science (In All but Name)

John Graunt (1620–1674), a pioneer in the field of demographic analysis, experienced financial difficulties in London and was on the verge of bankruptcy.²⁰ His work became the basis for analyzing longevity and death in a population group—or cohort—of people of the same age.²¹ This became the basis for the original life table developed by none other than Edmond Halley, who is far more famous because of the Halley’s comet than his contribution to actuarial science history.²²

Halley’s work included a method of using his life table to calculate the premium someone of a given age should pay to purchase an insurance product,²³ a concept today’s actuaries still use.

At this point in history, conditions were ripe for a more formal definition of the actuarial profession. The creation of actuarial science could well be officially marked in 1693, when Halley published a paper on the analysis of mortality tables.²⁴

Origin of the Title “Actuary”

When we look at the history of actuarial science, the commercial world was slow to adopt the techniques Halley and others proposed. The late 17^th to early 18^th centuries saw various developments in England that led to the demand for a title for the individuals who were essentially performing actuarial tasks.

British actuary James Dodson’s work on the level premium system led to a scientific calculation of premium rates. The Amicable Life Assurance Society originally refused Dodson admission because he was more than 45 years old.²⁵ But with his pioneering outline and the efforts of those who applied Dodson’s methods after his death in 1757, actuarial theory became working practice in 1762 when the Equitable Life Assurance Society was formed.²⁶

The Equitable Life Assurance Society put Dodson’s principles into practice²⁷ through a group of mathematicians that included Edward Rowe Mores.²⁸ After Dodson’s death, Mores became the leader of the group, and he specified that the chief official who would drive the use of these scientific methods would be called an actuary, a pivotal moment in the history of actuarial science.²⁹

The word “actuary” was derived from the Latin actuarius, for which there could be two meanings: a shorthand writer and one who writes out accounts.³⁰ According to studies, the actuarius in ancient Rome may have compiled various acta, or legislative enactments of the emperor, for public use.³¹ The Encyclopaedia Britannica stated that actuarii were officers who maintained military accounts.³²

A list of definitions included in The Oxford English Dictionary from the 16^th to 19^th centuries³³ includes definitions of the term to mean a registrar or clerk, a managing secretary or accountant of a public company, or an official in an insurance office whose duty it is to compile statistical tables of mortality and estimate necessary rates of premiums. These definitions evolved over the centuries, marking a shift in the meaning of the term. The definition of “actuary” today, of course, is far wider.

Foundations of the Actuarial Profession

Public recognition of actuaries came with:

• The Act of 1819
• The creation of the post of actuary to the National Debt Office in 1821
• The first actuarial appointment in government service: John Finlaison, the first president of the Institute of Actuaries, was actuary to the National Debt Office from 1822 to 1851^34,35

In the 19^th century, various technical improvements were introduced in the methods used to graduate mortality tables. In 1901, two actuaries, H.W. Manly and E.C. Thomas, wrote the first comprehensive paper on the valuation of staff pension funds in which they produced a multiple decrement table³⁶ that incorporated withdrawals and retirements. In 1952, Frank Redington produced his classic paper on immunization theory.

A Brief Look at the History of Actuarial Science in the United States

In 1735, the Friendly Society was established in Charleston, South Carolina, making it the first insurance company in the United States.³⁷ It went out of business a mere five years later. In 1752, Benjamin Franklin and his fellow firefighters founded the Philadelphia Contributionship,³⁸ the oldest insurer still operating in the United States.³⁹

American mathematician Elizur Wright suggested the formation of an actuarial organization in 1859, but the attempt failed, apparently on the grounds of professional mistrust and secrecy.⁴⁰ In 1889, when the Actuarial Society of America was set up with 38 initial members, there were fewer than 100 actuaries in North America.⁴¹

In 1895, the first woman member of the Actuarial Society, Emma Warren Cushman of Boston, was elected.⁴² In 1896, an actuarial examination system was adopted, with the first fellow by examination qualifying in 1900. Collaboration with global actuaries grew steadily, and the Fourth International Congress convened in New York in 1903.

Today’s Actuary

Today’s actuary continues to manage financial risks, design products, calculate premiums and derive capital and reserving requirements, remaining true to past definitions of the title. However, actuaries today have a much broader scope of work and are often involved in banking, wealth management and government roles, ensuring societal well-being and security for their companies, investors, customers and the general public.⁴³

Following the collapse of companies such as the Equitable Life Assurance Society in the early 21^st century, the illustrious history of the society led by pioneers who coined the term “actuary” in 1762 wound down. This brought a focus to risk management, independent review, upholding professional integrity and fairness to customers.

According to the Bureau of Labor Statistics, insurance companies or consultancies continue to employ most actuaries, but the actuarial scope of work is reaching increasingly new horizons. Actuaries now are heavily involved in software companies, artificial intelligence (AI) and data science and have increased their focus on climate change and sustainability.

Key Lessons From the History of Actuarial Science

It is worth reflecting on some of the observations from the history of actuarial science:

• Some of the concepts we use today in actuarial science are far older than we might think. For example, the concepts of risk sharing and insurance have existed for millennia—this calls for more frequent innovation in the future.
• Several times in history, the world has been slow to react to new techniques, often needing multiple breakthroughs or repeated discovery and continuous improvements.
• Significant developments in the industry may occur in informal settings, such as the discussions in London coffeehouses in the 17^th century.
• Pioneers whose discoveries transform the profession may at times be exploring an area beyond their primary area of expertise, as did the well-known astronomer Halley.
• Questions about the identity of an actuary have existed since time immemorial. Are we business professionals, scientists or a hybrid? This did not stop innovation in the past, so we should not dwell on it too much—especially if creating new actuarial techniques is solving real-world problems.
• Most industries see cycles of rapid development and stagnation. I assert we should expect new techniques in climate risk assessment, AI and cybersecurity to similarly see peaks and troughs in public interest and the speed of future advances.

We typically may think of the history of actuarial science spanning a couple of centuries, with most technological advances restricted to the past few decades. However, a closer look at actuarial science history reveals a far longer and richer heritage led by pioneers who went beyond personal constraints and showed the way for future generations.

Today’s actuaries should suggest novel actuarial methods if it benefits the profession and should not get discouraged if public recognition of their achievements is slow. The scientific techniques underlying the actuarial profession have evolved to include probability and statistics, risk management and efficient use of technologies, and we should welcome further change with the times.

Statements of fact and opinions expressed herein are those of the individual authors and are not necessarily those of the Society of Actuaries or the respective authors’ employers.

Copyright © 2024 by the Society of Actuaries, Chicago, Illinois.