可持续的中国城乡居民养老保险体系的数学模型研究

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

对可持续的中国城乡居民养老保险体系的数学模型进行了研究.结合实际、较全面地确定了影响养老保险的相关指标,并分层次地建立养老保险指标体系的指标体系图1.针对问题1,根据全面性、层次性、规律性、预测辅助性、可持续性的原则,分别建立了新农保、城职保个人账户、城职保社会统筹、企业基金的收入与支出模型,改进了周渭兵、王晓军教授的模型,进而构建了养老保险金模型.该模型结合实际,考虑因素较全面,分层次,体现了"多缴多得,长缴多得"的基本规则.针对问题2,对养老保险金模型进行MATLAB编程,基于题所给数据,并查询大量资料,考虑了通货膨胀,改良了平均工资年均增长率G_r,得到更符合实际的仿真结果.考虑倍增计划,改变了平均工资年均增长率G_r、养老金年均增长率k.发现国家需要将k的取值适当下调以弥补养老保险金的缺口.针对问题3,分析了各国不同养老保险模式的优劣,结合我国国情,利用MATLAB进行了仿真,寻找合理替代率、缴费率与养老保险体系可持续性之间的关系.使用观察法,控制变量法,定义了判断替代率、缴费率区间是否合理的判断函数l.提出应对矛盾尖锐期的三种政策:适时调整基本养老保险缴费率;控制物价指数、适时降低养老金年均增长率;建立多层次的养老保险体系.经过仿真预测发现,这三种政策对推迟"缺口"时间的来临,减小了"缺口",加快养老保险良性循环有积极作用.针对问题4,增加了可调节变量α、γ,建立了自适应养老保险金模型.其中k=α-γ,使得养老金年均增长率k的确定有了科学依据,是自适应的,而不是决策者拍脑袋决定的.建立了多层次、考虑因素较全面、相对结合国情的一系列模型,意在为"可持续"的中国城乡居民养老保险体系设计提供相对客观数据支撑与辅助决策.然而,我国的养老保险制度本身就存在很多缺陷,相关统计的数据亦并不全面.根据具一定缺陷制度建立的模型,又使用不完全正确的数据进行预测,得到的结果往往只是一个养老保险金的发展趋势,甚至是一个错误的发展趋势,而绝不可能是一个完全正确、精确的解.因此,模型只能用来辅助决策,而我国的养老保险体系完善还需要良性的政策激励,任重而道远.

In this paper, the mathematical model on sustainable pension system for Chinese urban and rural residents were studied. Combined with practical situation, we comprehen- sively 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 Insur- ance for Urban Residents model, income and expenditure model of enterprise funds, improv- ing 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,~ 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~ 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 hmction 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 a, % establish adaptive pension model. k = a- 7 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.