The origins of actuarial science lie in the seventeenth century. During this period, commercial needs gave rise to transactions involving compound interest, marine insurance was commonplace and the algebra of life annuities came into existence. Indeed, valuation techniques for financial transactions were known even in ancient Roman times and became of increasing importance as world trade developed after 1300.During the 16th Century, some of the European writers on arithmetic such as Simon Stevin and Jan Trenchant devoted some space to elementary problems in compound interest. There were no actuaries in the formal sense at that time. The nearest equivalent was the mathematical practitioner, a consultant who would tackle all kinds of problems on request from commercial matters to navigation. Richard Witt was one such; he practised in London in the early 1600s and wrote the first comprehensive book in English on compound interest. But Witt's book did not venture into life insurance mathematics and it was not until later in the 17th Century that the necessary tools became available. One such was the developing science of probability; another was the concept of the life table based on mortality investigations, the first published example being that of John Graunt in 1662.Thus, by 1670 two of the main foundations of actuarial science were firmly in place: compound interest; probability theory and the life table. These tools were employed almost immediately by the Dutch prime minister, Jan de Witt, to investigate the value of the Government life annuities. But his treatise, although of considerable merit, remained unnoticed for many years and did not influence the development of actuarial science. Then, in 1693 Edmund Halley, the British mathematician, published his famous Royal Society paper, describing the construction of the life table from observations. He also set down the method for valuing life annuities, which is, in essence, the same as that used today.Actuarial science had thus arguably been born, and by 1700 the way was open for the techniques to be applied for commercial purposes. At this time, life annuities were bought and sold freely, although in the main their values were not properly calculated. Life assurance consisted mainly of short term risk-only contracts purchased by single premium from and individual underwriter, the premiums being assessed on the basis of the underwriter's experience and judgement, but with no formal scientific basis. Early in the 18th Century the Amicable Society established life assurance on a basis which involved some build-up of funds or reserves.Some of the pioneers in the 1700s and 1800s were eminent scientists and mathematicians who became interested in actuarial problems. Thus, we find Leonhard Euler, James and Daniel Bernoulli, Carl Friedrich Gauss, Abraham de Moivre, Benjamin Gompertz becoming involved in the science and making significant contributions. In the U.K., many papers on actuarial matters were read before the Royal Society, there being no other formal theater for discussion.The 1800s saw the establishment of may life assurance companies in the U.K. and elsewhere, operating on a scientific basis following the pioneering work of James Dodson and Richard Price. A wide range of level annual premium contracts was available to the public. Annuities were calculated by proper methods and the dangers of inappropriate mortality tables became known. Life insurance mathematics, compound interest and probability theory were then at an advanced state of development, and mortality tables had developed from crude tabulations of deaths to property calculated and considered works. The first table of life assurance mortality from pooled data was published in 1843, as also was English Life Table No. 1, for the national population. The collection and analysis of sickness statistics were under way, but the level of attainment was still fairly crude.By the mid nineteenth century, a considerable amount of fundamental work had been completed. There then followed a rapid expansion in the refinement and practical application of actuarial theory. Life insurance business was expanding rapidly and many actuaries were employed in the industry on a full-time basis. The Institute of Actuaries was established in 1848 and the Faculty of Actuaries in 1856, providing the first dedicated actuarial publication media, respectively the Journal and the Transactions. The first text books began to appear for assisting students to pass professional examinations. A steady stream of significant papers on actuarial theory and practice was published in these journals, together with translations of significant contributions from continental Europe.A statutory system of actuarial supervision of life insurance began with Massachusetts legislative session of 1858 and the Life Assurance Companies Act of 1870 in the U.K. This latter piece of legislation was the first detailed statutory framework regulating the life assurance business, Parliament having chosen the freedom with publicity principle; this led to debates on the relative merits of the bonus reserve and the net premium valuation methods. The 1860s had earlier seen the invention of the contribution method of the distribution of surplus, almost universally used in life assurance practice in North America. In the U.S., the Actuarial Society of America was founded in 1880, the forerunner of the Society of Actuaries and the Casualty Actuarial Society in 1914.Among the significant contributions of the period up to the early part of our century is the appearance of Makeham's formula for the force of mortality which was found able to represent faithfully much published mortality data for the next 100 years. We also find the development of different approaches to graduation; the publication of premium conversion tables which eased the burden of calculating life insurance premiums in the days before calculating machines became generally available; the development of analysis of surplus, whereby the causes of the surplus or deficiency emerging in any type of valuation can be revealed and further analysed; the development of risk and credibility theory; the development of the mathematical theory of multiple decrement and multiple state models; the systematic presentation of pension fund valuation ideas and formulae; the formulation of the principles of institutional investment; the agreement on a standard actuarial notation which provided a language to facilitate international dialogue. We also note the important creation of the International Actuarial Association in 1895 which over the last 100 years has fostered and encouraged the development of actuarial ideas and the actuarial profession around the world, and has provided a forum for international meetings and the cross-fertilisation of ideas.
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