During the last two decades,quantification and management of longevity risks have become an active issue in both public pension plans and life insurance companies.

At the moment,scholars both domestic and overseas have not yet established a set of research results which are both standardized and systematic,and in combination with quantitative analysis.The most basic or core work in quantifying longevity risks is the research on the methods of modeling mortality rates.Currently,the quantitative research on longevity risks concentrates mainly on investigating various dynamic mortality rates models for prediction.In summary,based on the fitting and smoothing effects with respect to the available mortality rates at various ages,dynamic mortality rates models mainly involve two problems,i.e.,age extrapolation and trend forecast.As regards these two problems,there are still plenty of deficiencies in current studies.The deficiencies are mainly classified into four parts as follows.First,the analysis of modeling oldest-old mortality rates is still not thorough enough,in other words,the reasonable quantification of the indexes of tail risks of the survival distribution is not available.Second,there are few studies on birth cohort effect of mortality rates.Third,gender difference,population difference,regional difference and national difference of mortality rates have not been explored in a consistent modeling framework.Finally,there are no systematic research in the following aspects,such as the comparison and selection of various dynamic mortality rates models,the applicability and robustness of different models.

Accurate estimates of mortality rates at advanced old ages are crucial for predicting life expectancies,population size of the oldest-old age group,and mortality rates.Therefore,in the present monograph we systemati cally collate the existing problems with ideas for modifications and improvements as regards methods of modeling dynamic mortality rates,both domestic and overseas; also we summarize various models and methods of quantifying longevity risks.Specifi cally,we integrate the extreme modeling method for oldest-old mortality rates and the hierarchi cal modeling framework,and propose some dynamic mortality rates modeling approach,in order to fill up the deficiency of the previous studies.In the present monograph we propose three dynamic mortality rates models,which are applied to all ages together,with young,old,and advanced old inclusive,using China's mortality data from 1994 to 2010 by gender.These models are proposed from a hierarchi cal modeling perspective,and based on a piecewise form by combining the Lee-Carter model and generalized Pareto distribution.We obtain the optimal hierarchi cal model,and compare the optimal hierarchi cal model and the Lee-Carter model as regards the goodness-of-fit and the predictive power.The empiri cal results indicate that the optimal hierarchi cal model provides very accurate short-term prediction from 2011 to 2012.The optimal model provides better modifications to the relatively rough estimates at advanced old ages resulted from the LeeCarter model.We also make conclusions that the advanced old men have been more selective than the advanced old women as far as survival of the fittest is concerned,and the gender difference in the average life expectancy at birth is gradually narrowing.Finally,as some applications of the optimal model,for all ages in the entire life span we investigate and show the dynamic evolutions of mortality rates,survival distributions,distributions of age at death,and average life expectancies for male and female respectively from 1994 to 2060 in China,and construct dynamic life tables by gender based on the period data.Moreover,we quantify the inherent longevity risks on annuity products of insurance companies in China.Based on these aforementioned investigations,in combination with the applications and development of management tools of overseas longevity risks,mainly the theoreti cal research and practi cal experience with respect to natural hedging for both annuity and life insurance products of insurance companies,reinsurance,and longevity risks securitization,we further discuss the feasibility and possible existing problems in implementation in China,in order to provide countermeasures and suggestions for building quantitative assessment system on longevity risks in China.

Specifi cally,the contents of this monograph are organized as follows.The monograph is divided into seven chapters.Chapter 1 is the introduction and motivation of the monograph.We innovatively propose to study modeling dynamic mortality rates for old-age,oldest-old and all ages in the entire life spans separately in China.Based on these studies,we have completed two parts of the most basic work of longevity risks quantification,i.e.modeling dynamic mortality rates and constructing dynamic life tables.They are investigated in chapter 2,3 and 4 respectively.Furthermore,we extend to measure the impacts of longevity risks on pricing and liability reserving for both life insurance and annuity products of China's insurance companies.They are included in chapter 5 and 6 respectively.Chapter 7 is the summary and concluding remarks.We also point out clearly some ideas and directions for further research.

In summary,coping with aging of the global population is an urgent,pragmatic,and systematic project.The most important and fundamental task of this project is to estimate reasonably and demonstrate effectively dynamic evolutions of populations covering all ages,i.e.young age,old-age and oldest-old at the entire life span,for all countries in the world.The main contribution of the monograph is that we have systemati cally conducted the work of modeling China's dynamic mortality graduation,age extrapolation and trends forecast for all ages within the entire life cycle.Using the optimal hierarchi cal dynamic mortality rates models at all ages,which are motivated by the study,we further reveal the dynamic evolutions of mortality rates,survival distributions,distributions of age at death,and average life expectancies within the entire life cycle for male and female respectively from 1994 to 2060 in China,and construct dynamic life tables by gender based on the period data.With the aforementioned studies,we have comprehensively quantified the impacts of longevity risks on pricing and liability reserving of life insurance companies in China.The present fundamental research has formed for the first time Chinese mortality rates data across all ages at the entire life span,which is comparable to HMD.This has great significance to the accumulation of basic population data in China,which provides data and methods support for selective reference and transplantation of those policies from the developed countries to deal with aging issue.The proposed research methods in the present monograph are expected to be directly applied to the quantification and management of longevity risks in three-pillar pension plan（i.e.,the basic pension plan,supplementary pension plan,and individual commercial pension insurance）.We also hope that these exploratory studies are helpful to provide some more accurate and more scientific basis for related public policies in the aging process.

It is worth pointing out that the research involves a large amount of complex numeri cal calculation,which is largely attributed to the support of increasingly sophisticated computer technology and statisti cal software.R language is free development software,which is increasingly popular in current international community and has many packages.For hierarchi cal modeling dynamic mortality rates at old ages and oldest-old ages,and even all ages at the entire life spans,we applies R for complete programming in the present monograph.All algorithms are modular and have a high level of flexibility and portability.R software is increasingly widespread with applications in financial engineering,quantitative risk management,statistics and actuarial science and so on.It has become a development trend to solve various numeri cal problems using R software.

Key Words: Dynamic Mortality Rates Models; Longevity Risks;Extreme Modeling Methods; Hierarchi cal Models; Liability Reserving