In modern life insurance, the basic tool of annuity risk assessment, reserve calculations and premium calculations is the mortality table. Models of life tables are incorporated into life insurance, annuity and pension calculations. This is a relatively recent development. Although forms of insurance are known to have existed as early as the second century, the first mortality table was constructed by John Graunt in 1662. Since then, actuarial science research has occupied itself with developing, improving and extending the forecasting accuracy of mortality rates and life tables.
This special issue continues the mortality-modeling tradition, focusing on the creation of better-fitting or better-forecasting models of mortality. In “A Three-Factor Model for Mortality Modeling,” Vincenzo Russo and colleagues describe the creation of a mortality model involving three factors, as opposed to the single factor, age, used by the classical mortality tables. In “Compression of Morbidity and Mortality: New Perspectives,” Eric Stallard reviews the concepts of mortality compression and morbidity compression, describes how they are related, and empirically examines changes in mortality compared with changes in morbidity. Other articles in this issue address likely future changes in mortality. In “Life Expectancy in 2040: What Do Clinical Experts Expect?” Canudas-Romo and colleagues describe the results of asking medical experts to assess life expectancy in 2040; the forecasts point to increasing life expectancy due to mortality changes. In “Causes-of-Death Mortality: What Do We Know on Their Dependence?” Arnold (-Gaille) and Sherris analyze five causes of death in 10 countries, finding a long-run equilibrium relationship between the causes of death but substantial differences across countries. Finally, in “Familial Risk for Exceptional Longevity,” Sebastiani and colleagues use a network model to compute the increased chance for exceptional longevity, conditional on the subject’s family history of longevity. In summary, this special issue continues the advancement of mortality modeling and discusses its relationship to problems involving longevity risk.
Patrick L. Brockett, Editor
Articles from 2015
The North American Actuarial Journal - Volume 19, Issue 2 2015
Séverine Arnold (-Gaille) & Michael Sherris
Over the last century, the assumption usually made was that causes of death are independent, although it is well-known that dependancies exist. Recent developments in econometrics allow, through Vector Error Correction Models (VECMs), to model multivariate dynamic systems including time dependency between economic variables. Common trends that exist between the variables may then be highlighted, the relation between these variables being represented by a long-run equilibrium relationship. In this work, VECMs are developed for causes-of-death mortality. We analyze the five main causes of death across 10 major countries representing a diversity of developed economies. The World Health Organization website provides cause-of-death information for about the last 60 years. Our analysis reveals that long-run equilibrium relationships exist between the five main causes of death, improving our understanding of the nature of dependence between these competing risks over recent years. It also highlights that countries usually had different past experience in regard to cause-of-death mortality trends, and, thus, applying results from one country to another may be misleading.
The North American Actuarial Journal - Volume 19, Issue 2 2015
Vincenzo Russo, Rosella Giacometti, Svetlozar Rachev & Frank J. Fabozzi
In this article, we propose a three-factor model for mortality modeling in which the dynamic of the entire term structure of mortality rates can be expressed in closed form as a function of three variables x, t, and y. Due to this feature, we are able to project mortality rates across age (x), across time (t), and for y years (y ≥ 1) after t. Our proposal differs from most existing models where only the one-year mortality rate is considered (y = 1). The model is characterized by three parameters that are calibrated yearly. We describe the stochastic dynamic of the three factors with correlated autoregressive processes. We generate stochastic scenarios accounting for the historical mortality trend in a consistent manner with the Gompertz law. Using population mortality data for Italy, the U.S., and the U.K., the model’s forecasting capability is assessed, and a comparative analysis with other models is provided
Articles from 2016
The North American Actuarial Journal - Volume 20, Issue 1 2016
Paola Sebastiani, Stacy L. Andersen, Avery I. McIntosh, Lisa Nussbaum, Meredith D. Stevenson, Leslie Pierce, Samantha Xia, Kelly Salance & Thomas T. Perls
One of the most glaring deficiencies in the current assessment of mortality risk is the lack of information concerning the impact of familial longevity. In this article we update estimates of sibling relative risk of living to extreme ages using data from more than 1700 sibships, and we begin to examine the trend for heritability for different birth-year cohorts. We also build a network model that can be used to compute the increased chance for exceptional longevity of a subject, conditional on his or her family history of longevity. The network includes familial longevity from three generations and can be used to understand the effects of paternal and maternal longevity on an individual's chance to live to an extreme age.
The North American Actuarial Journal - Volume 20, Issue 3 2016
Vladimir Canudas-Romo, Eva DuGoff, Albert W. Wu, Saifuddin Ahmed & Gerard Anderson
We use expert clinical and public health opinion to estimate likely changes in the prevention and treatment of important disease conditions and how they will affect future life expectancy. Focus groups were held including clinical and public health faculty with expertise in the six leading causes of death in the United States. Mortality rates and life tables for 2040 were derived by sex and age. Life expectancy at age 20 and 65 was compared to figures published by the Social Security Administration and to estimates from the Lee-Carter method. There was agreement among all three approaches that life expectancy at age 20 will increase by approximately one year per decade for females and males between now and 2040. According to the clinical experts, 70% of the improvement in life expectancy will occur in cardiovascular disease and cancer, while in the last 30 years most of the improvement has occurred in cardiovascular disease. Expert opinion suggests that most of the increase in life expectancy will be attributable to the already achieved reduction in smoking rates, especially for women.
The North American Actuarial Journal - Volume 20, Issue 4 2016
Compression of morbidity is a reduction over time in the total lifetime days of chronic disability, reflecting a balance between (1) morbidity incidence rates and (2) case-continuance rates, generated by case-fatality and case-recovery rates. Chronic disability includes limitations in activities of daily living and cognitive impairment, which can be covered by long-term-care insurance. Morbidity improvement can lead to a compression of morbidity if the reductions in age-specific prevalence rates are sufficiently large to overcome the increases in lifetime disability due to concurrent mortality improvements and progressively higher disability prevalence rates with increasing age. Compression of mortality is a reduction over time in the variance of age at death. Such reductions are generally accompanied by increases in the mean age at death; otherwise, for the variances to decrease, the death rates above the mean age at death would need to increase, and this has rarely been the case. Mortality improvement is a reduction over time in the age-specific death rates and a corresponding increase in the cumulative survival probabilities and age-specific residual life expectancies. Mortality improvement does not necessarily imply concurrent compression of mortality. This article reviews these concepts, describes how they are related, shows how they apply to changes in mortality over the past century and to changes in morbidity over the past 30 years, and discusses their implications for future changes in the United States. The major findings of the empirical analyses are the substantial slowdowns in the degree of mortality compression over the past half century and the unexpectedly large degree of morbidity compression that occurred over the morbidity/disability study period 1984–2004; evidence from other published sources suggests that morbidity compression may be continuing.