| With the development and changes of science and technique, and the increasing level of health, medical and social services, people’s average life expectancy is increasing year by year. Since the family planning of our country was put forward, it has been more than thirty years. The influence of neonate control has been shown to population structure; Our population is in the aging forward situation. Under the existing social system, on the one hand, the number of staff nearing retirement still have strong abilities to work, resulting in a current retirees re-employment heat; On the other hand, Social security can’t maintain balance on its own because of the increased pressure. Therefore, under the he current social background, the study of the retirement age adjustment has a very important significance to many fields such as human resources utilization and stability of social security.Using the urban population as object of research, from the law of population growth, and using the fractional step method, this article established a quantitative mathematical model based on population growth and the balance of short-term pension funds, and the best retirement age in the next15years obtained in solving this model by the MATLAB software.Firstly, the urban population status and development trends of our country since2000years were obtained by the literature search method. The age growth of population state model, which contains the urbanization rate and other factors, was established by sub-element method. With numerically solving the mathematical model by MATLAB, the total urban population of different ages to2025years was predicted, and the population trends from2000to2025years were given.Secondly, the factors affecting retirement age were analyzed for the operation status quo of social endowment insurance fund. From the angle of the stable operation of the Pension Fund in China, the mathematical models of retirement age were established, which based on individual stability and a stable in medium-short term for pension. Through solving this model by the MATLAB software, the optimal retirement age and its development trend were obtained, which based on the point of social security.The main results of this study were described as follows:1. China’s aging population become more and more serious, pension payments pressure followed by it is also growing.2. In order to maintain the stable operation of the pension in medium-short term, the optimal legal retirement age is62years old (When the retirement of the men and women is the same age), or the retirement age of man is65years old (The retirement age of is60years old).3. Currently our country’s retirement age is made in the1980s, and it is in a low state. From the respective of easing the pressure of pension payments, postponing the retirement age can be considered.From the short-term balance of the pension insurance fund, this model studied quantitively the issue of optimal retirement age setting, which is based on the dynamic development model of population by the fractional step and dynamic balance of payments model, so the model has strong portability and scalability. But population development problems has three special characteristics, such as sequence inertia, random and non-linear, it caused that initial value have obviously effect upon the model. Therefore it made the model to have some limitations. |
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