Forecasting Future Mortality Trends and Longevity North American Actuarial Journal

North American Actuarial Journal

Virtual Special Issue of NAAJ:

Forecasting Future Mortality Trends and Longevity


by Patrick L. Brockett, Editor

The basic tool of modern life insurance and annuity risk assessment—and rigorous reserve calculations and premium calculations—is the mortality table, also referred to as a life table by those exhibiting a more optimistic vocabulary. This table of death likelihoods, cross-classified by age and sex, can be used to obtain a probability distribution for the (uncertain) time until death for an individual. This is then used to determine the expected net present value (or fair value) of the specified death benefit to be provided, where discounting occurs from the (uncertain) time of death, using the time value of money and the death probability at each age. Models of life tables are now incorporated fundamentally into life insurance, annuity and pension calculations and for other purposes, such as structured legal settlements.

Insurance and models of mortality were not always connected this way. Insurance existed long before the invention of probability and statistics or the creation of life tables. While a rigorous approach to probability was first developed around 1654 in a series of letters between Blaise Pascal and Pierre de Fermat, early precursors of what might now be construed as life insurance existed as early as 100 BC in burial clubs for Roman soldiers and poor people.[1] Club members pitched in to pay for proper burial of diseased members who lacked the capacity to pay for their own burial—a worthwhile cause, given the common belief at the time that if no proper burial took place, the ghost of the dead would continue to haunt the living. “Premiums,” or the amount to contribute, were not determined mathematically; at best, they were wagers or bets about mortality. The same guess or wager approach to premium determination also applied to actual written legal contracts for life insurance.[2] Life (or mortality) tables were the first step in making these calculations objectively determined. The Equitable Life Assurance Society (Equitable Life), founded in 1762, pioneered the transition from premium guesses and wagers, showing how to determine age-based premiums based on mortality tables to set insurance premiums in the scientific manner used today.

Developing, improving and extending the forecasting accuracy of mortality rates and life tables has occupied actuarial science research since the first mortality table was constructed by John Graunt in 1662 (Natural and Political Observations Made upon the Bills of Mortality).  Subsequently, Edmond Halley in 1693 showed how to construct an empirical mortality table



[1] For example, the Roman military leader Caius Marius created such a burial club for his troops in 100 BC.
[2] The oldest formally written life insurance policy seems to have been issued in London in 1583. It was a one-year policy on the life of William Gybbon, with Richard Martin as beneficiary. Martin paid 30 pounds sterling and was to receive 400 pounds sterling if Gybbon died within the year. Interestingly, he did die near the end of the policy term, and the issuers of the policy refused payment, contending that they defined  a “year” as 12 lunar months of 28 days (which totals 336 days), not a solar year of 365 days. The issuers’ ignoble assertion was rightly rejected in court, and they had to pay. Other interesting examples of pre-probability life insurance contracts can be found in the insurance library at Saint John’s University in New York City. These include an insurance policy taken out on the queen of England (essentially a wager).


more rigorously and use it to price annuities scientifically and rationally. The now-common mathematical functional form approach to mortality table construction—along with its use to price insurance and annuities—was originated by the notable mathematician Abraham de Moivre who created the first mathematical mortality model for utilization in calculating annuity values.  This parametric functional form approach to mortality table constriction was subsequently extended by Gompertz and Makeham and others.

This special issue continues this important mortality-modeling tradition. The insurance process is forward focused—future benefits being paid based on future mortality. Therefore, the static mortality table approach of Halley, de Moivre, Gompertz and Makeham must be augmented by a forecasting of mortality into the future. The creation of better-fitting or better-forecasting models of mortality continues to this day and is a subject of advancements presented in this special issue.
In “A Three-Factor Model for Mortality Modeling,” Vincenzo Russo, Rosella Giacometti, Svetlozar Rachev and Frank J. Fabozzi address this challenge in mortality modeling by creating a more complex mortality model involving three factors, as opposed to the single factor, age, used by the classical mortality tables. The authors perform fit to mortality data from several countries and assess the ability to forecast mortality.
In the next article, “Compression of Morbidity and Mortality: New Perspectives,” Eric Stallard addresses an important issue related to the evolution of mortality tables over time. People are living longer (longevity risk), so the end points of mortality tables are extending, but the financial impact of this change in mortality is closely related to morbidity evolution and its relationship to mortality evolution—i.e., whether these additional years of life are spent in relatively good health or in a disabled state, requiring more resources. This article reviews the concepts of mortality compression and morbidity compression, describes how they are related, and empirically examines changes in mortality over the past century compared with changes in morbidity over the past 30 years. Empirically, Stallard finds substantial slowdowns in the degree of mortality compression over the past half century and an unexpectedly large degree of morbidity compression in the aged 65 and over U.S. population from 1984 to 2004 in a study \ including both community and institutional participants, with the latter making major and often neglected contributions to population morbidity.  He also discusses implications.

A major aspect of using a mortality model for financial calculations is the determination of what changes in mortality are likely to occur in the future, and why. Other articles in this issue address this topic. Longevity risk—the risk of outliving resources, due to decreased mortality rates caused by medical and societal changes—is a significant and increasingly important consideration for the insurance industry, pension funds, social security systems and society. To delineate the characteristics of this longevity risk problem, “Life Expectancy in 2040: What Do Clinical Experts Expect?” describes the results of asking medical experts to assess life expectancy in 2040, as opposed to using a mathematical forecasting technique. The findings of the article’s authors—Vladimir Canudas-Romo, Eva DuGoff, Albert W. Wu, Saifuddin Ahmed and Gerard Anderson—suggest that for both males and females, the life expectancy at age 20 will increase by approximately one year per decade between now and 2040, with 70 percent of the improvement being due to mortality changes in cardiovascular disease and cancer.
In light of the above mentioned findings about the significance of causes of mortality like cardiovascular disease and cancer in determining ultimate life expectancy in the future, the question arises as to what interactions exist between various different causes of death (i.e., does reduction in one cause interact with a reduction in another, and how does this in turn effect ultimate aggregate mortality).  Traditionally different causes of death are assumed to act independently over time in statistical models of mortality to produce death, although dependency in the effect of different causes has been previously recognized. This statistical dependence among causes of death mortality is addressed in the next paper, “Causes-of-Death Mortality: What Do We Know on Their Dependence?” by Séverine Arnold (-Gaille) and Michael Sherris. Knowing there is cause-of-death dependence, and being able to mathematically model such dependence, allows for improved mortality risk assessment compared to the current process of assuming statistical independence among the causes of death within a competing risk setting. Arnold (-Gaille) and Sherris examine dependence among five causes of death across 10 countries and find a long-run equilibrium relationship between these five causes of death. There were, however, substantial differences across countries, implying that extrapolating results from one country to another may be misleading.
In the final article, “Familial Risk for Exceptional Longevity,” Paola Sebastiani, Stacy L. Andersen, Avery I. McIntosh, Lisa Nussbaum, Meredith D. Stevenson, Leslie Pierce, Samantha Xia, Kelly Salance and Thomas T. Perls address longevity risk from the perspective of a history of longevity in close family members. They use a network model to compute the increased chance for exceptional longevity of a subject, conditional on his or her family history of longevity. This naturally has implications for longevity risk modeling of the individual (or pension or annuity provider) that goes beyond current mortality-table-based pricing methods.
In summary, this special issue continues the advancement of mortality modeling and discusses its relationship to problems involving longevity risk . The issues of rigorously modeling mortality evolution over time and of payment for the financial consequences of mortality changes (longevity risk) remain among the most highly researched topics in actuarial science of life and health insurers and social planners.