Optimal Neighborhood Selection for AR-ARCH Random Fields with Application to Mortality

This article proposes an optimal and robust methodology for model selection. The model of interest is a parsimonious alternative framework for modeling the stochastic dynamics of mortality improvement rates introduced recently in the literature. The approach models mortality improvements using a random field specification with a given causal structure instead of the commonly used factor-based decomposition framework. It captures some well-documented stylized facts of mortality behavior including: dependencies among adjacent cohorts, the cohort effects, cross-generation correlations, and the conditional heteroskedasticity of mortality. Such a class of models is a generalization of the now widely used AR-ARCH models for univariate processes. A the framework is general, it was investigated and illustrated a simple variant called the three-level memory model. However, it is not clear which is the best parameterization to use for specific mortality uses. In this paper, we investigate the optimal model choice and parameter selection among potential and candidate models. More formally, we propose a methodology well-suited to such a random field able to select thebest model in the sense that the model is not only correct but also most economical among all thecorrectmodels. Formally, we show that a criterion based on a penalization of the log-likelihood, e.g., the using of the Bayesian Information Criterion, is consistent. Finally, we investigate the methodology based on Monte-Carlo experiments as well as real-world datasets.

PRICING LONGEVITY-LINKED SECURITIES IN THE PRESENCE OF MORTALITY TREND CHANGES

ABSTRACT Even though the trend in mortality improvements has experienced several permanent changes in the past, the uncertainty regarding future mortality trends is often left unmodeled when pricing longevity-linked securities. In this paper, we present a stochastic modeling framework for the valuation of longevity-linked securities which explicitly considers the risk of random future changes in the long-term mortality trend. We construct a set of meaningful probability distortions which imply equivalent risk-adjusted pricing measures under which the basic model structure is preserved. Inspired by risk-based capital requirements for (re)insurers, we also establish a cost-of-capital pricing approach which then serves as the appropriate reference framework for finding a reasonable range for the market price of longevity risk. In a numerical application, we demonstrate that our model produces plausible risk loadings and show that a greater proportion of the risk loading is allocated to longer maturities when the risk of random future mortality trend changes is adequately modeled.

Leaders and Laggards in Life Expectancy Among European Scholars From the Sixteenth to the Early Twentieth Century

When did mortality first start to decline, and among whom? We build a large, new data set with more than 30,000 scholars covering the sixteenth to the early twentieth century to analyze the timing of the mortality decline and the heterogeneity in life expectancy gains among scholars in the Holy Roman Empire. The large sample size, well-defined entry into the risk group, and heterogeneity in social status are among the key advantages of the new database. After recovering from a severe mortality crisis in the seventeenth century, life expectancy among scholars started to increase as early as in the eighteenth century, well before the Industrial Revolution. Our finding that members of scientific academies—an elite group among scholars—were the first to experience mortality improvements suggests that 300 years ago, individuals with higher social status already enjoyed lower mortality. We also show, however, that the onset of mortality improvements among scholars in medicine was delayed, possibly because these scholars were exposed to pathogens and did not have germ theory knowledge that might have protected them. The disadvantage among medical professionals decreased toward the end of the nineteenth century. Our results provide a new perspective on the historical timing of mortality improvements, and the database accompanying our study facilitates replication and extensions.

Trends in ischaemic heart disease and cerebrovascular disease mortality in Europe: an observational study from 1990–2017

Background Cardiovascular disease remains the leading cause of death worldwide. Previously, we identified a growing disparity between Western and Eastern European countries for mortality from ischaemic heart disease (IHD) and cerebrovascular disease (CVD). Purpose To describe current trends in mortality from IHD and CVD. Methods IHD and CVD age-standardized death rates (ASDR) for European countries between 1990–2017 were extracted from the World Health Organization mortality database using the International Classification of Diseases 9th and 10th Edition codes. Jointpoint regression analysis was used to describe trends over this period. Results Between 1990–2017, IHD mortality declined in all included countries except Croatia (+3% in males and +23% in females). Largest mortality improvements were generally seen in Western European countries, including the Netherlands, UK and Sweden, which saw greater than 65% improvements for both sexes. Estonia was a notable exception, which, after the Netherlands, demonstrated the second highest improvement in mortality (−69% in males, −74% in females). Hungary and Greece saw the smallest improvements in IHD mortality (approximately −12% to −27%). Results of jointpoint regression analysis for selected European countries are shown in Figure 1. In 2017 Lithuania had the highest mortality rate in both males and females (279.4/100,000 and 261.3/100,000, respectively) whilst the Netherlands had the lowest mortality in males and females (32.6/100,00 and 15.3/100,000, respectively). This represents an approximately 8.5-fold difference in IHD mortality in males and a 10.5-fold difference in females between these two countries. CVD mortality declined in all included countries between 1990–2017. Estonia saw the greatest improvements in both males and females (−80.8% and −84.9%, respectively), followed by Austria, Portugal and the Czech Republic (over 70% reductions in both sexes). Bulgaria, Romania and Lithuania saw the smallest reductions (approximately −17% to −33%). In 2017, Bulgaria had the highest CVD mortality rate in both males and females (149.9/100,000 and 113.1/100,000, respectively), whilst the lowest mortality rate was observed in Austria (21.8/100,000 and 19.5/100,000 for males and females, respectively). This represents an approximately 7-fold difference in CVD mortality in males and a 6-fold difference in females between these two countries. Conclusions IHD and CVD mortality rates continue to decrease for men and women across Europe. While certain Eastern European countries have demonstrated considerable mortality improvements over this observation period, in general the disparity between Eastern and Western Europe persists, with further work required to understand and address these inequalities. Squares: male. Circles: female Funding Acknowledgement Type of funding source: None

FORECASTING MORTALITY FOR KAZAKHSTAN AND ASSESSING IT’S IMPACT ON THE STATE PENSION SPENDING

This paper uses the mortality projection methods of Knykova A. and Sapin A., based on the original Lee-Carter model, in order to investigate mortality rates for Kazakhstan for the time period from 2018 to 2025 and assess their impact on the state pension spending in Kazakhstan. The results show that improvements in mortality rates have been increasing the number of years that people spend in retirement in Kazakhstan, which directly affects the public pension spending. The overall state pension spending is expected to increase in Kazakhstan from 2019 to 2025, reflecting the gradually increasing effect of mortality improvements, but the state pension spending’s share of GDP is projected to decline from 2021 to 2024. However, extra expenditures of the government on pensions due to future mortality improvements will increase gradually as a share of GDP over time and reach 0,02% in 2024

Trends in disease incidence and survival and their effect on mortality in Scotland: nationwide cohort study of linked hospital admission and death records 2001–2016

ObjectivesIdentify causes and future trends underpinning Scottish mortality improvements and quantify the relative contributions of disease incidence and survival.DesignPopulation-based study.SettingLinked secondary care and mortality records across Scotland.Participants1 967 130 individuals born between 1905 and 1965 and resident in Scotland from 2001 to 2016.Main outcome measuresHospital admission rates and survival within 5 years postadmission for 28 diseases, stratified by sex and socioeconomic status.Results‘Influenza and pneumonia’, ‘Symptoms and signs involving circulatory and respiratory systems’ and ‘Malignant neoplasm of respiratory and intrathoracic organs’ were the hospital diagnosis groupings associated with most excess deaths, being both common and linked to high postadmission mortality. Using disease trends, we modelled a mean mortality HR of 0.737 (95% CI 0.730 to 0.745) from one decade of birth to the next, equivalent to a life extension of ~3 years per decade. This improvement was 61% (30%–93%) accounted for by improved disease survival after hospitalisation (principally cancer) with the remainder accounted for by lowered hospitalisation incidence (principally heart disease and cancer). In contrast, deteriorations in infectious disease incidence and survival increased mortality by 9% (~3.3 months per decade). Disease-driven mortality improvements were slightly greater for men than women (due to greater falls in disease incidence), and generally similar across socioeconomic deciles. We project mortality improvements will continue over the next decade but slow by 21% because much progress in disease survival has already been achieved.ConclusionMorbidity improvements broadly explain observed mortality improvements, with progress on prevention and treatment of heart disease and cancer contributing the most. The male–female health gaps are closing, but those between socioeconomic groups are not. Slowing improvements in morbidity may explain recent stalling in improvements of UK period life expectancies. However, these could be offset if we accelerate improvements in the diseases accounting for most deaths and counteract recent deteriorations in infectious disease.