This book provides good coverage of longevity and mortality modeling from the basic mathematics to recently developed models as well as risk management. The theory presented is wide ranging, including topics such as deterministic annuity valuation and hedging using longevity bonds. Although the audience of the book is composed primarily of advanced undergraduate students, postgraduate students and practicing actuaries, the material presented is relevant to industry practitioners wanting an understanding of longevity risk models. The book requires a modeling background and an interest in understanding longevity models and applications. Furthermore, this book would be of interest to advanced economics and finance students as well as pension economists. Researchers with a background in pensions and insurance would also find this book a useful and well presented reference of the major issues attracting research efforts on longevity modeling.
Longevity risk and its modeling, although an area of actuarial research and practice for many decades and dating, as mentioned in the preface, back to the 1600's, has shown a significant increase in research interest in the last 15 to 20 years. This can be traced to the increased usage of life annuity products in pension plans due to the progressive shift from defined benefit to defined contribution plans. This has furthermore coincided with the ageing of the population around the world and the recognition that mortality risk, of which longevity risk is an element, cannot merely be managed through the law of large numbers as was traditionally the case. Pension funds and life insurers issuing annuity products with guarantees related to mortality have faced increasing costs and have had to apply more sophistication in the management of these risks. At the same time regulators are encouraging insurers to use internal models to quantify risk and assess risk based capital.
The book starts with a basic review of deterministic life annuity mathematics and annuity contracts, and covers basic actuarial models, including graduation and heterogeneity in mortality. This leads into a discussion of mortality trends for both the general population and insured lives based on Belgian data. An introduction to mortality forecasting follows, which includes the basic ideas underlying the Lee-Carter model as well as brief mention of issues such as cohort models and cause of death. Following that is a deeper coverage of age-period models based on the Lee-Carter and Cairns-Blake-Dowd models as well as a discussion of P-splines. Belgian data is again used for the application of the models. Uncertainty of projections, including confidence intervals and fan charts, are also briefly introduced. The models are then extended to cover age-period-cohort considerations with application to UK mortality data. Finally a substantial section, comprising over a quarter of the book, studies the risk management of longevity, including hedging, reinsurance, securitization as well as some pricing and solvency topics under the title of actuarial perspectives. There is a brief, and useful, listing of further references at the end of most chapters.
There are few books in the area of longevity modeling. A related text is the book by Moshe Milevsky entitled The Calculus of Retirement Income (Cambridge University Press, 2006) which provides a broad consideration of the economics of uncertainty in mortality. The actuarial texts are inadequate since the uncertainty usually presented is for lifetimes under the assumption of known future mortality rates and independent (and identically distributed) lives of the same age. This is not the case as evidenced by past experience and hence more sophisticated modeling and risk management techniques are required. This book would be an excellent text for use by professional actuarial associations. Longevity risk and its modeling should be given more prominence in the professional actuarial syllabus due to its increased relevance. Furthermore, this is an area of research and practice that other professionals are active in, including economists, risk management and insurance researchers and practitioners, as well as an increasing number of finance professionals. The book is at a level for professionals or researchers from these areas with a quantitative background.
The book's strengths are its widespread coverage from the basic to some of the more advanced aspects of longevity modeling. The analysis of the trends in mortality and longevity would have benefited from taking a broader perspective and providing an overview of experience in a wider range of countries. Issues around the projection of mortality and resulting uncertainty are also based on extrapolation from historical data and there is no substantial discussion of methods of considering future uncertainties not captured in historical data. It was at times surprising to note the authors' lack of consideration given to the underlying drivers of past mortality trends when the extrapolation of these trends was being advocated. Given the recent events in financial markets and reliance on credit risk models without a broader understanding of their limitations, coverage of the limitations of these models and how this could be managed would have been a valuable addition to a book such as this.
The products considered are guaranteed products and there is no discussion of alternative risk pooling arrangements such as group self annuitization. There is substantial coverage of quantification of longevity risk and solvency issues as well as capital market products to manage the risk. In contrast to a very short discussion of the impact of systematic longevity risk improvement on pricing, a crucial aspect of writing guaranteed life annuity business (unless with-profit based).
The book is not a research monograph. There are many topics in longevity modeling not covered in the book. The financial approach to pricing that has been explored in research is only mentioned in a few paragraphs although references are included. This deserved more prominence and coverage particularly with the development in financial markets such as q-forwards and longevity swaps.
The authors have done an excellent job in bringing together coverage on topics of current interest and providing a modern approach to mortality modeling not found in the actuarial textbooks.
