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The field of financial mathematics has developed tremendously over the past thirty years, and the underlying models that have taken shape in interest rate markets and bond markets, being much richer in structure than equity-derivative models, are particularly fascinating and complex. This book introduces the tools required for the arbitrage-free modelling of the dynamics of these markets. Andrew Cairns addresses not only seminal works but also modern developments. Refreshingly broad in scope, covering numerical methods, credit risk, and descriptive models, and with an approachable sequence of opening chapters, Interest Rate Models will make readers--be they graduate students, academics, or practitioners--confident enough to develop their own interest rate models or to price nonstandard derivatives using existing models. The mathematical chapters begin with the simple binomial model that introduces many core ideas. But the main chapters work their way systematically through all of the main developments in continuous-time interest rate modelling. The book describes fully the broad range of approaches to interest rate modelling: short-rate models, no-arbitrage models, the Heath-Jarrow-Morton framework, multifactor models, forward measures, positive-interest models, and market models. Later chapters cover some related topics, including numerical methods, credit risk, and model calibration. Significantly, the book develops the martingale approach to bond pricing in detail, concentrating on risk-neutral pricing, before later exploring recent advances in interest rate modelling where different pricing measures are important.
Mortality improvements, uncertainty in future mortality trends and the relevant impact on life annuities and pension plans constitute important topics in the field of actuarial mathematics and life insurance techniques. In particular, actuarial calculations concerning pensions, life annuities and other living benefits (provided, for example, by long-term care insurance products and whole life sickness covers) are based on survival probabilities which necessarily extend over a long time horizon. In order to avoid underestimation of the related liabilities, the insurance company (or the pension plan) must adopt an appropriate forecast of future mortality. Great attention is currently being devoted to the management of life annuity portfolios, both from a theoretical and a practical point of view, because of the growing importance of annuity benefits paid by private pension schemes. In particular, the progressive shift from defined benefit to defined contribution pension schemes has increased the interest in life annuities with a guaranteed annual amount. This book provides a comprehensive and detailed description of methods for projecting mortality, and an extensive introduction to some important issues concerning longevity risk in the area of life annuities and pension benefits. It relies on research work carried out by the authors, as well as on a wide teaching experience and in CPD (Continuing Professional Development) initiatives. The following topics are dealt with: life annuities in the framework of post-retirement income strategies; the basic mortality model; recent mortality trends that have been experienced; general features of projection models; discussion of stochastic projection models, with numerical illustrations; measuring and managing longevity risk.
This open access book collects expert contributions on actuarial modelling and related topics, from machine learning to legal aspects, and reflects on possible insurance designs during an epidemic/pandemic. Starting by considering the impulse given by COVID-19 to the insurance industry and to actuarial research, the text covers compartment models, mortality changes during a pandemic, risk-sharing in the presence of low probability events, group testing, compositional data analysis for detecting data inconsistencies, behaviouristic aspects in fighting a pandemic, and insurers' legal problems, amongst others. Concluding with an essay by a practicing actuary on the applicability of the methods proposed, this interdisciplinary book is aimed at actuaries as well as readers with a background in mathematics, economics, statistics, finance, epidemiology, or sociology.
During the last 25 years, life expectancy at age 50 in the United States has been rising, but at a slower pace than in many other high-income countries, such as Japan and Australia. This difference is particularly notable given that the United States spends more on health care than any other nation. Concerned about this divergence, the National Institute on Aging asked the National Research Council to examine evidence on its possible causes. According to Explaining Divergent Levels of Longevity in High-Income Countries, the nation's history of heavy smoking is a major reason why lifespans in the United States fall short of those in many other high-income nations. Evidence suggests that current obesity levels play a substantial part as well. The book reports that lack of universal access to health care in the U.S. also has increased mortality and reduced life expectancy, though this is a less significant factor for those over age 65 because of Medicare access. For the main causes of death at older ages-cancer and cardiovascular disease-available indicators do not suggest that the U.S. health care system is failing to prevent deaths that would be averted elsewhere. In fact, cancer detection and survival appear to be better in the U.S. than in most other high-income nations, and survival rates following a heart attack also are favorable. Explaining Divergent Levels of Longevity in High-Income Countries identifies many gaps in research. For instance, while lung cancer deaths are a reliable marker of the damage from smoking, no clear-cut marker exists for obesity, physical inactivity, social integration, or other risks considered in this book. Moreover, evaluation of these risk factors is based on observational studies, which-unlike randomized controlled trials-are subject to many biases.
Almost 25 years have passed since the Demography of Aging (1994) was published by the National Research Council. Future Directions for the Demography of Aging is, in many ways, the successor to that original volume. The Division of Behavioral and Social Research at the National Institute on Aging (NIA) asked the National Academies of Sciences, Engineering, and Medicine to produce an authoritative guide to new directions in demography of aging. The papers published in this report were originally presented and discussed at a public workshop held in Washington, D.C., August 17-18, 2017. The workshop discussion made evident that major new advances had been made in the last two decades, but also that new trends and research directions have emerged that call for innovative conceptual, design, and measurement approaches. The report reviews these recent trends and also discusses future directions for research on a range of topics that are central to current research in the demography of aging. Looking back over the past two decades of demography of aging research shows remarkable advances in our understanding of the health and well-being of the older population. Equally exciting is that this report sets the stage for the next two decades of innovative researchâ€"a period of rapid growth in the older American population.
Modern mortality modelling for actuaries and actuarial students, with example R code, to unlock the potential of individual data.
It is a challenging task to read the balance sheet of an insurance company. This derives from the fact that different positions are often measured by different yardsticks. Assets, for example, are mostly valued at market prices whereas liabilities are often measured by established actuarial methods. However, there is a general agreement that the balance sheet of an insurance company should be measured in a consistent way. Market-Consistent Actuarial Valuation presents powerful methods to measure liabilities and assets in a consistent way. The mathematical framework that leads to market-consistent values for insurance liabilities is explained in detail by the authors. Topics covered are stochastic discounting with deflators, valuation portfolio in life and non-life insurance, probability distortions, asset and liability management, financial risks, insurance technical risks, and solvency.
In 1950 men and women in the United States had a combined life expectancy of 68.9 years, the 12th highest life expectancy at birth in the world. Today, life expectancy is up to 79.2 years, yet the country is now 28th on the list, behind the United Kingdom, Korea, Canada, and France, among others. The United States does have higher rates of infant mortality and violent deaths than in other developed countries, but these factors do not fully account for the country's relatively poor ranking in life expectancy. International Differences in Mortality at Older Ages: Dimensions and Sources examines patterns in international differences in life expectancy above age 50 and assesses the evidence and arguments that have been advanced to explain the poor position of the United States relative to other countries. The papers in this deeply researched volume identify gaps in measurement, data, theory, and research design and pinpoint areas for future high-priority research in this area. In addition to examining the differences in mortality around the world, the papers in International Differences in Mortality at Older Ages look at health factors and life-style choices commonly believed to contribute to the observed international differences in life expectancy. They also identify strategic opportunities for health-related interventions. This book offers a wide variety of disciplinary and scholarly perspectives to the study of mortality, and it offers in-depth analyses that can serve health professionals, policy makers, statisticians, and researchers.
As the United States and the rest of the world face the unprecedented challenge of aging populations, this volume draws together for the first time state-of-the-art work from the emerging field of the demography of aging. The nine chapters, written by experts from a variety of disciplines, highlight data sources and research approaches, results, and proposed strategies on a topic with major policy implications for labor forces, economic well-being, health care, and the need for social and family supports.