可持续的中国城乡居民养老保险体系的数学模型研究

考虑了替代率、缴费率、人口结构、分年龄段死亡率、经济增速、财政补贴、工资水平、投资效益,引入收缴率、通货膨胀率等当今影响养老保险的活跃因素,建立了"城乡结合"的中国城乡基本养老保险收支跨期叠代模型,并在此基础上进行优化.通过仿真,探讨了替代率和缴费率的合理区间.

The Research of Mathematical Model on Sustainable Pension System for Chinese Urban and Rural Residents

In this paper,the mathematical model on sustainable pension system for Chinese urban and rural residents were studied.Combined with practical situation,we comprehensively determine the effects of pension-related indicators and hierarchically establish indicator system of pension in Figure 1.For question 1,according to a comprehensive,layered,regularity,prediction auxiliary,sustainability principle,We establish Rural Residents Insurance model,the Old-Age Insurance for Urban Residents model,income and expenditure model of enterprise funds,improving Zhou Weibing and Wang Xiaojun Professor's model,and then build a pension model.The model combines reality,considers comprehensive factors,and reflects the basic rule—— "Pay more for much,pay more for longer".For question 2,we have emulated the mathematical model of pension system based on the given data by MATLAB programming.Taking into account inflation,we have looked up large amounts of data,improved the value of G_r which denotes the average annual growth rate of wages and finally got the results of more realistic simulation Considering double plan,we have changed G_r the value of k,which denotes the average annual growth rate of pension,we have discovered that our country need to find the appropriate values of k to cover the pension gap For question 3,we have analyzed the advantages and disadvantages different models of different countries' pension.Combined with Chinese national conditions,we use MATLAB to simulate to find the relationship among the reasonable replacement rate,contribution rate and pension system sustainability.We use observation,the method of control variables and define the function l which determine whether the range of replacement rate or the contribution rate is reasonable.At last,we propose three policies to solve contradiction:the timely adjustment of the basic pension insurance contribution rate;controlling price index timely reducing the annual growth rate of pension;establishing a multi-level pension insurance system Through simulations,we have found that the three policies have a positive effect of postponing the arrival of "gap",reducing the "gap" and speeding up the virtuous cycle of pension insurance For question 4,We add adjustable variables α,γ,establish adaptive pension model.k = α-γ,making the determination of average annual growth rate of pension has a scientific basis,is adaptive,rather than rack decision makers' brains.In this paper,We establish a series of multi-level,more comprehensive,relatively combining Chinese condition models,intend to provide a relatively objective data support and assist decision-making for the design of sustainable Pension System for Chinese Urban and Rural Residents.However,there are many defects in China's pension system,and relevant statistical data are not comprehensive.According a certain defect system to establish model,and use not entirely correct data to predict,the result is often just a pension trends,or even a wrong trend,and never could be a completely correct and accurate solution.Thus,our model can be used to assist decision-making,but improving our pension system needs a benign policy incentive.We have long way to go.