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**Modelling longevity dynamics for pensions and annuity business.**
*(English)*
Zbl 1163.91005

Oxford: Oxford University Press (ISBN 978-0-19-954727-2/hbk). xix, 395 p. (2009).

The presented book addresses actual problems of mortality improvements (longevity) and its impact to pension and annuity business. It 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. The book consists of seven main parts (chapters). The following topics are dealt with: life annuities in the framework of post-retirement income strategies; the basic mortality model; recent mortality trends; general features of projection models; a discussion of stochastic projection models, with numerical illustrations; and measuring and managing longevity risk.

Chapter 1 has an introductory nature and provides an overview of basic types of life annuities. In Chapter 2, a basic mortality model is introduced and concepts, such as age continuous mortality framework, indices of lifetime probability distribution, main mortality laws, models for mortality at old ages are presented. In Chapter 3, basic mortality trends during XX century are summarized. In Chapter 4 introduction to basic mortality forecasting methods is given. Idea of dynamic mortality is introduced, mortality projection by extrapolation and (briefly) by interpolation are described, brief explanation of well known Lee Carter mortality projection method is given. Ideas given in Chapters 5 and 6 expand those given in Chapter 4. In Chapter 5 age-period framework is discussed as well as Lee-Carter log-bilinear and Cairns–Blake–Dowd mortality projection models are presented. In Chapter 6 mortality forecasting models are further extended with incorporation of cohort effect. In the last - 7 Chapter some basic longevity risk management tools are described. Numerical illustrations to some presented problems are given, also some chapters include suggestions for further reading. Ideas presented in this book may be addressed as one of top problems in annuity and insurance business. The book will be useful for academics and practitioners as well as other interested readers.

Chapter 1 has an introductory nature and provides an overview of basic types of life annuities. In Chapter 2, a basic mortality model is introduced and concepts, such as age continuous mortality framework, indices of lifetime probability distribution, main mortality laws, models for mortality at old ages are presented. In Chapter 3, basic mortality trends during XX century are summarized. In Chapter 4 introduction to basic mortality forecasting methods is given. Idea of dynamic mortality is introduced, mortality projection by extrapolation and (briefly) by interpolation are described, brief explanation of well known Lee Carter mortality projection method is given. Ideas given in Chapters 5 and 6 expand those given in Chapter 4. In Chapter 5 age-period framework is discussed as well as Lee-Carter log-bilinear and Cairns–Blake–Dowd mortality projection models are presented. In Chapter 6 mortality forecasting models are further extended with incorporation of cohort effect. In the last - 7 Chapter some basic longevity risk management tools are described. Numerical illustrations to some presented problems are given, also some chapters include suggestions for further reading. Ideas presented in this book may be addressed as one of top problems in annuity and insurance business. The book will be useful for academics and practitioners as well as other interested readers.

Reviewer: Jonas Šiaulys (Vilnius)

### MSC:

91-02 | Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance |

91B30 | Risk theory, insurance (MSC2010) |