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Author Pitacco, Ermanno
Title Modelling Longevity Dynamics for Pensions and Annuity Business
Imprint Oxford : Oxford University Press, Incorporated, 2009
©2009
book jacket
Descript 1 online resource (416 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Note Intro -- Contents -- Preface -- 1 Life annuities -- 1.1 Introduction -- 1.2 Annuities-certain versus life annuities -- 1.2.1 Withdrawing from a fund -- 1.2.2 Avoiding early fund exhaustion -- 1.2.3 Risks in annuities-certain and in life annuities -- 1.3 Evaluating life annuities: deterministic approach -- 1.3.1 The life annuity as a financial transaction -- 1.3.2 Actuarial values -- 1.3.3 Technical bases -- 1.4 Cross-subsidy in life annuities -- 1.4.1 Mutuality -- 1.4.2 Solidarity -- 1.4.3 'Tontine' annuities -- 1.5 Evaluating life annuities: stochastic approach -- 1.5.1 The random present value of a life annuity -- 1.5.2 Focussing on portfolio results -- 1.5.3 A first insight into risk and solvency -- 1.5.4 Allowing for uncertainty in mortality assumptions -- 1.6 Types of life annuities -- 1.6.1 Immediate annuities versus deferred annuities -- 1.6.2 The accumulation period -- 1.6.3 The decumulation period -- 1.6.4 The payment profile -- 1.6.5 About annuity rates -- 1.6.6 Variable annuities and GMxB features -- 1.7 References and suggestions for further reading -- 2 The basic mortality model -- 2.1 Introduction -- 2.2 Life tables -- 2.2.1 Cohort tables and period tables -- 2.2.2 'Population' tables versus 'market' tables -- 2.2.3 The life table as a probabilistic model -- 2.2.4 Select mortality -- 2.3 Moving to an age-continuous context -- 2.3.1 The survival function -- 2.3.2 Other related functions -- 2.3.3 The force of mortality -- 2.3.4 The central death rate -- 2.3.5 Assumptions for non-integer ages -- 2.4 Summarizing the lifetime probability distribution -- 2.4.1 The life expectancy -- 2.4.2 Other markers -- 2.4.3 Markers under a dynamic perspective -- 2.5 Mortality laws -- 2.5.1 Laws for the force of mortality -- 2.5.2 Laws for the annual probability of death -- 2.5.3 Mortality by causes -- 2.6 Non-parametric graduation
2.6.1 Some preliminary ideas -- 2.6.2 The Whittaker-Henderson model -- 2.6.3 Splines -- 2.7 Some transforms of the survival function -- 2.8 Mortality at very old ages -- 2.8.1 Some preliminary ideas -- 2.8.2 Models for mortality at highest ages -- 2.9 Heterogeneity in mortality models -- 2.9.1 Observable heterogeneity factors -- 2.9.2 Models for differential mortality -- 2.9.3 Unobservable heterogeneity factors. The frailty -- 2.9.4 Frailty models -- 2.9.5 Combining mortality laws with frailty models -- 2.10 References and suggestions for further reading -- 3 Mortality trends during the 20th century -- 3.1 Introduction -- 3.2 Data sources -- 3.2.1 Statistics Belgium -- 3.2.2 Federal Planning Bureau -- 3.2.3 Human mortality database -- 3.2.4 Banking, Finance, and Insurance Commission -- 3.3 Mortality trends in the general population -- 3.3.1 Age-period life tables -- 3.3.2 Exposure-to-risk -- 3.3.3 Death rates -- 3.3.4 Mortality surfaces -- 3.3.5 Closure of life tables -- 3.3.6 Rectangularization and expansion -- 3.3.7 Life expectancies -- 3.3.8 Variability -- 3.3.9 Heterogeneity -- 3.4 Life insurance market -- 3.4.1 Observed death rates -- 3.4.2 Smoothed death rates -- 3.4.3 Life expectancies -- 3.4.4 Relational models -- 3.4.5 Age shifts -- 3.5 Mortality trends throughout EU -- 3.6 Conclusions -- 4 Forecasting mortality: an introduction -- 4.1 Introduction -- 4.2 A dynamic approach to mortality modelling -- 4.2.1 Representing mortality dynamics: single-figures versus age-specific functions -- 4.2.2 A discrete, age-specific setting -- 4.3 Projection by extrapolation of annual probabilities of death -- 4.3.1 Some preliminary ideas -- 4.3.2 Reduction factors -- 4.3.3 The exponential formula -- 4.3.4 An alternative approach to the exponential extrapolation -- 4.3.5 Generalizing the exponential formula -- 4.3.6 Implementing the exponential formula
4.3.7 A general exponential formula -- 4.3.8 Some exponential formulae used in actuarial practice -- 4.3.9 Other projection formulae -- 4.4 Using a projected table -- 4.4.1 The cohort tables in a projected table -- 4.4.2 From a double-entry to a single-entry projected table -- 4.4.3 Age shifting -- 4.5 Projecting mortality in a parametric context -- 4.5.1 Mortality laws and projections -- 4.5.2 Expressing mortality trends via Weibull's parameters -- 4.5.3 Some remarks -- 4.5.4 Mortality graduation over age and time -- 4.6 Other approaches to mortality projections -- 4.6.1 Interpolation versus extrapolation: the limit table -- 4.6.2 Model tables -- 4.6.3 Projecting transforms of life table functions -- 4.7 The Lee-Carter method: an introduction -- 4.7.1 Some preliminary ideas -- 4.7.2 The LC model -- 4.7.3 From LC to the Poisson log-bilinear model -- 4.7.4 The LC method and model tables -- 4.8 Further issues -- 4.8.1 Cohort approach versus period approach. APC models -- 4.8.2 Projections and scenarios. Mortality by causes -- 4.9 References and suggestions for further reading -- 4.9.1 Landmarks in mortality projections -- 4.9.2 Further references -- 5 Forecasting mortality: applications and examples of age-period models -- 5.1 Introduction -- 5.2 Lee-Carter mortality projection model -- 5.2.1 Specification -- 5.2.2 Calibration -- 5.2.3 Application to Belgian mortality statistics -- 5.3 Cairns-Blake-Dowd mortality projection model -- 5.3.1 Specification -- 5.3.2 Calibration -- 5.3.3 Application to Belgian mortality statistics -- 5.4 Smoothing -- 5.4.1 Motivation -- 5.4.2 P-splines approach -- 5.4.3 Smoothing in the Lee-Carter model -- 5.4.4 Application to Belgian mortality statistics -- 5.5 Selection of an optimal calibration period -- 5.5.1 Motivation -- 5.5.2 Selection procedure -- 5.5.3 Application to Belgian mortality statistics
5.6 Analysis of residuals -- 5.6.1 Deviance and Pearson residuals -- 5.6.2 Application to Belgian mortality statistics -- 5.7 Mortality projection -- 5.7.1 Time series modelling for the time indices -- 5.7.2 Modelling of the Lee-Carter time index -- 5.7.3 Modelling the Cairns-Blake-Dowd time indices -- 5.8 Prediction intervals -- 5.8.1 Why bootstrapping? -- 5.8.2 Bootstrap percentiles confidence intervals -- 5.8.3 Application to Belgian mortality statistics -- 5.9 Forecasting life expectancies -- 5.9.1 Official projections performed by the Belgian Federal Planning Bureau (FPB) -- 5.9.2 Andreev-Vaupel projections -- 5.9.3 Application to Belgian mortality statistics -- 5.9.4 Longevity fan charts -- 5.9.5 Back testing -- 6 Forecasting mortality: applications and examples of age-period-cohort models -- 6.1 Introduction -- 6.2 LC age-period-cohort mortality projection model -- 6.2.1 Model structure -- 6.2.2 Error structure and model fitting -- 6.2.3 Mortality rate projections -- 6.2.4 Discussion -- 6.3 Application to United Kingdom mortality data -- 6.4 Cairns-Blake-Dowd mortality projection model: allowing for cohort effects -- 6.5 P-splines model: allowing for cohort effects -- 7 The longevity risk: actuarial perspectives -- 7.1 Introduction -- 7.2 The longevity risk -- 7.2.1 Mortality risks -- 7.2.2 Representing longevity risk: stochastic modelling issues -- 7.2.3 Representing longevity risk: some examples -- 7.2.4 Measuring longevity risk in a static framework -- 7.3 Managing the longevity risk -- 7.3.1 A risk management perspective -- 7.3.2 Natural hedging -- 7.3.3 Solvency issues -- 7.3.4 Reinsurance arrangements -- 7.4 Alternative risk transfers -- 7.4.1 Life insurance securitization -- 7.4.2 Mortality-linked securities -- 7.4.3 Hedging life annuity liabilities through longevity bonds -- 7.5 Life annuities and longevity risk
7.5.1 The location of mortality risks in traditional life annuity products -- 7.5.2 GAO and GAR -- 7.5.3 Adding FIexibility to GAR products -- 7.6 Allowing for longevity risk in pricing -- 7.7 Financing post-retirement income -- 7.7.1 Comparing life annuity prices -- 7.7.2 Life annuities versus income drawdown -- 7.7.3 The 'mortality drag' -- 7.7.4 Flexibility in FInancing post-retirement income -- 7.8 References and suggestions for further reading -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- R -- S -- T -- U -- V -- W -- X -- Y
A text aimed at researchers and postgraduates actuarial science, statistics, and actuarial mathematics providing a comprehensive and detailed description of statistical methods for projecting mortality, and an extensive discussion of some important issues concerning the longevity risk in the area of life annuities and pension benefits
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Pitacco, Ermanno Modelling Longevity Dynamics for Pensions and Annuity Business Oxford : Oxford University Press, Incorporated,c2009 9780199547272
Subject Life insurance -- Mathematics.;Mortality -- Tables
Electronic books
Alt Author Denuit, Michel
Haberman, Steven
Olivieri, Annamaria
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