Preface

Some understanding and preliminary results of my study on population aging problem are included in this book. Population aging is a serious problem in developed countries for recent two decades, on the one hand, social security systems fell into difficulty situation, on the other hand, it effects economy on many fields:research and develop, consumption demands, and labor market. Studying on population aging in our country has a practical meaning, because we are developing country now, the social security in our country will confront more difficult situation than developed countries. Thus, how to solve this problem is very important in the change period of economy develop.

Some policies for population aging are considered in this book. Our government changed the only child policy to permit two children in every family last year. It was an important change on population policies in our country since 1980's. For the fertility problem, I will study in a separated book later.

In this book, the author consider the other policies for population aging problem: optimal retire time and the demand for life insurance. As an individual, how long time he should work to prepare his retire expending is also an important plan for himself. For the income what earned in his working time, he also has to consider how to distribute his income for saving and life insurance to supplement the shortage of the social security. Thus, those problems are important not only for the government and insurance companies but also for the individuals. The models and analyses in chapter 4 and 5 are new and considered by myself.

This book includes five chapters. In Chapter 1, some problems of population aging are discussed and literatures on this problem are given. In Chapter 2, some models in Macroeconomics are mentioned, the models in continuous time, the models in discrete time, overlapping generation models are discussed. In Chapter 3, some important papers on uncertain life time and life insurance demands are discussed. I every paper, I have given proofs and explanation in detail. In Chapter 4, analyses on the optimal retire time are discussed both in the continuous time model and in the discrete time model, in the discrete time model the effect of retire time is analyzed. In Chapter 5, an overlapping generation model is established to study the demand of life insurance, the effects of other factors on life insurance demands, for instance, popular aging, the changes on social security, and changes of interest rate. In the Appendix, optimal control theory is given, which will be used in the book.

This book was supported by the MOE Project of Key Research Institute of Humanities and Social Science in Universities 15JJD790037 of the Ministry of Education of the Peoples'Republic of China. I also appreciate the leadership of our institute for their support on writing of this book.

Ling Qi

China Institute for Actuarial Science

Central University of Finance and Economics

April 4, 2017