This year marks the bicentennial of Benjamin Gompertz’s groundbreaking paper, On the Nature of the Function Expressive of the Law of Human Mortality, presented to the Royal Society on 16 June 1825. For two centuries, Gompertz’s insights have shaped how we understand longevity risk—a cornerstone of retirement planning. As superannuation funds and financial advisers grapple with the challenges of an ageing population, Gompertz’s work remains as relevant as ever. 

The Birth of a Mortality Revolution 

Gompertz, a self-taught mathematician and actuary, set out to quantify the increasing likelihood of death as we age. “His eponymous law showed that mortality rates increase exponentially as we age. This simple yet profound observation became foundational to actuarial science. 

This equation not only provided a mathematical basis for life tables but also transformed the pricing of life insurance and annuities by linking age to probabilistic risk. 

The Gompertz curve helped formalise life tables, revolutionised life insurance and annuity pricing, and enabled actuaries to link age with probabilistic risk. At its heart, the model acknowledged a powerful truth: human mortality follows a broadly predictable trajectory. For retirees and those managing pension systems, this predictability has become a powerful tool to manage the financial uncertainties of lifespan. 

Longevity Risk in Today’s Retirement Systems 

In today’s superannuation environment, longevity risk—the uncertainty around how long someone will live—presents a major challenge. Underestimating lifespan can lead to people running out of money, while overestimating it can result in overly cautious investment strategies or reduced income. 

Gompertz’s law didn’t merely describe mortality—it made it predictable. For the first time, actuaries could move beyond crude life tables to sophisticated mathematical models that captured the underlying structure of human mortality. 

The practical applications were transformative: 

• • Life Insurance Pricing: Insurers could now calculate premiums with unprecedented precision, matching risk to reward across different ages and populations. 

• • Annuity Valuation: The exponential nature of mortality risk allowed for more accurate pricing of annuities, laying the groundwork for modern retirement income products. 

• • Population Projections: Governments and institutions could forecast demographic changes with mathematical rigor, enabling better planning for social security systems and healthcare provision. 

By calibrating Gompertz-Makeham parameters to historical data, funds can forecast mortality trends and adjust reserves in real time. Recent research shows that integrating anticipated longevity improvements into annuity factors can help prevent payout reductions at older ages—a key concern as more retirees reach 90 and beyond. 

Evolving the Model for the 21st Century 

While the original Gompertz model has stood the test of time, modern demography and data have uncovered areas for refinement:   

1. 1. Mortality plateaus: At extreme ages (e.g., beyond 90), mortality rates tend to flatten rather than continue rising exponentially. Hybrid models now combine exponential and logistic elements to better reflect these patterns—particularly important for an ageing population. 
   2. Changing parameters: Analysis of 20th-century data shows Gompertz’s “ageing rate” parameter has decreased by around 1% annually, reflecting medical advances and lifestyle changes. Continuous recalibration ensures models stay relevant. 
   3. Stochastic projections: More advanced models incorporate randomness and systemic shocks (e.g. pandemics or medical breakthroughs). These are useful for stress-testing pension systems and ensuring resilience under a range of future scenarios. 

Strategic Implications for Retirement Planning 

Gompertz’s legacy continues to offer powerful, practical applications for superannuation funds, financial planners, and policymakers: 

• • Dynamic risk management: Longevity projections based on Gompertz principles can help funds better match assets to liabilities, blending growth assets with longevity-protected instruments like deferred annuities or pooled products. 

• • Efficiency through pooling: Larger member pools reduce individual (idiosyncratic) risk, but systematic trends—such as rising life expectancy—require mechanisms for intergenerational risk sharing. GSAs that update annuity factors based on real-time mortality data are a prime example. 

• • Better client conversations: Survival curves based on Gompertz modelling can help retirees visualise the uncertainty around lifespan, enabling more informed decisions about spending, saving, and when to access retirement products. 

Honouring the Past, Securing the Future 

Gompertz’s 1825 paper was more than a mathematical breakthrough—it was a blueprint for managing one of retirement’s greatest uncertainties: how long we live. Two centuries later, Gompertz’s insights remain remarkably relevant to contemporary challenges in superannuation and retirement planning. The model still underpins how we think about and address longevity risk. 

At Optimum Pensions, we believe the best way to honour Gompertz’s legacy is to continue refining, adapting, and applying his insights. That means developing solutions that combine actuarial rigour with practical innovation—ensuring retirees can spend with confidence, knowing their income will last as long as they do. 

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