Annuities upon Lives

Annuities upon Lives, published in 1725 by mathematician Abraham de Moivre, establishes mathematical methods for calculating life insurance and annuity rates. The book introduces probability theory concepts and applies them to financial and actuarial problems. De Moivre presents tables, formulas, and worked examples to demonstrate how to determine present values and future payments based on mortality data. The text addresses key questions faced by insurance companies and financial institutions regarding risk assessment and pricing of life-contingent contracts. The work includes sections on joint life annuities, reversionary payments, and the valuation of successive lives. De Moivre's mathematical framework draws upon his earlier discoveries in probability theory and introduces approximation techniques still relevant to modern actuarial science. This foundational text represents a bridge between abstract mathematics and practical financial applications, marking a crucial development in both probability theory and actuarial mathematics. The methodologies established in this work continue to influence modern approaches to financial risk management.

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A Treatise of Algebra by Colin Maclaurin This mathematical text explores probability theory and actuarial calculations through algebraic methods similar to de Moivre's approach.

The Doctrine of Chances by Abraham de Moivre This companion work expands on probability calculations with applications to mortality tables and life expectancy computations.

An Introduction to the Doctrine of Fluxions by William Emerson The text presents calculus methods that connect to probability and mortality calculations used in actuarial mathematics.

A Treatise on Life Insurance by James Dodson The work builds upon de Moivre's foundations to develop mathematical models for insurance premium calculations.

Theory of Interest by Stephen G. Kellison The book presents mathematical foundations of interest theory and mortality models used in modern actuarial science.

🔶 Abraham de Moivre wrote "Annuities upon Lives" (1725) while tutoring wealthy London merchants, making it one of the first practical guides for calculating life insurance and annuity rates. 🔶 The book introduced the concept of "expectation of life," which revolutionized actuarial science and is still fundamental to modern insurance mathematics. 🔶 De Moivre developed his famous "De Moivre's Law" in this work, suggesting that mortality increases in an arithmetic progression, which became a cornerstone of early actuarial calculations. 🔶 Despite being a brilliant mathematician, de Moivre lived in relative poverty and wrote this book partly to supplement his income by selling it to insurance companies and merchants. 🔶 The mathematical principles outlined in "Annuities upon Lives" helped establish London as the world's leading insurance market in the 18th century, a position it largely maintains today.