Benjamin Gompertz & the Gompertz Mortality Curve (1825)

Event Date: 1825 Category: Actuarial Science — Mortality Modeling / Mathematical Demography

Summary

Benjamin Gompertz (1779–1865) introduced a mathematical model of human mortality in 1825 that became the backbone of 19th‑century life‑insurance pricing. The Gompertz Law proposed that the force of mortality increases exponentially with age. This elegant model allowed actuaries to interpolate mortality rates, construct tables, and price life‑contingent products even when empirical data were incomplete.

Background / Context

By the early 19th century:

• insurers relied on empirical tables (e.g., Carlisle)
• data were often sparse at older ages
• actuaries needed a mathematical model to fill gaps

Gompertz, a self‑taught mathematician and Fellow of the Royal Society, provided the missing theoretical framework.

What Happened

⭐ 1. The Gompertz Law (1825)

Gompertz proposed that mortality follows the function:

μ(x) = Ae^{Bx} (force of mortality increases exponentially with age)

This captured the observed pattern that mortality accelerates in adulthood.

⭐ 2. Practical Applications

The Gompertz curve allowed actuaries to:

• smooth empirical mortality data
• extrapolate beyond observed ages
• construct complete mortality tables
• price annuities and life insurance more consistently

⭐ Sidebar: Why Gompertz Was a Breakthrough

The first mathematical model of human mortality

Gompertz gave actuaries:

• a continuous function
• a way to interpolate missing data
• a theoretical basis for mortality patterns
• a tool for pricing long‑term contracts

His model dominated actuarial science for nearly a century.

Impact

• Standardized mortality modeling
• Improved pricing consistency
• Enabled long‑term projections
• Influenced demography, biology, and public health

Why It Mattered (Plain English)

Gompertz answered a simple question with profound implications:

How does mortality increase with age? His answer gave actuaries a mathematical steering wheel.

Related Entries

• 1780s–1815 — The Carlisle Mortality Tables — empirical mortality foundations that Gompertz later modeled mathematically
• 1775–1776 — William Morgan, The First Actuarial Valuation (forthcoming) — early valuation work that predated mathematical mortality models
• 1848 — Founding of The Institute of Actuaries — the professional body that formalized mortality modeling, including Gompertz’s work
• 1860 — William Makeham & the Gompertz–Makeham Law — refinement of Gompertz’s model with an age‑independent hazard term
• 1870s–1890s — The American Adoption of Actuarial Science — U.S. insurers’ adoption of British mortality models, including Gompertz
• 1890s — Punch Cards for Mortality Tables — early mechanical computation that enabled large‑scale application of Gompertz curves
• 1930s–1950s — IBM Punch‑Card Computing & the Rise of Actuarial Automation — mechanized mortality modeling built on Gompertz foundations
• 1980s — The Birth of Catastrophe Modeling (AIR, RMS, EQE) — modern hazard‑modeling frameworks that descend from 19th‑century mortality models
• 1990s — Predictive Analytics Emerges in Insurance — multivariate modeling and early machine‑learning techniques extending the lineage of hazard‑based modeling
• 21st Century — Predictive Analytics & Machine Learning (forthcoming) — modern data‑science techniques that represent the full maturation of actuarial modeling