可持续的中国城乡居民养老保险体系数学模型

本文从我国现行养老金政策出发,利用灰关联分析得到养老金收支的影响因素的排序,建立中国城乡居民养老金收支模型.然后利用Logistic人口预测模型估计出不同替代率下2013-2035未来23年我国养老金缺口,并利用仿真方法算出保证我国养老保险体系的可持续性的替代率的合理区间为50%-70%.进一步分析影响替代率各因素的灵敏性,并考虑延迟退休、做实个人账户以及市场化投资等因素对模型进行改进.最后以养老金替代率为切入点,对退休年龄等模型参数的调整和有关措施进行了分析与评价.

Sustainable Mathematic Model of Chinese Urban and Rural Residents Pension Insurance System

Based on current pension policy of China, this paper first gets the sequence of various impact factors of the balance of payments by grey relational analysis. Secondly the static and dynamic models of Chinese urban and rural residents in pension payments are established. Then logistic prediction models are used to estimate the population replacement rate differenceof pension gap in the next 23 years ( from 2013 to 2035) . By comparison of different models of the world derive pension formula Chinese pension replacement rate, using simulation tools to compute, the reasonable range of alternatives rate pension system ensuring the sustainability is 50% -70%.Thirdly, considering the factors of the sensitivity affecting the replacement rate, delaying retirement, personal accounts do factor market investments, the model is improved. Finally taking the pension replacement rate as an entry point, the pension replacement rate model is refined, different retirement pension replacement rate and lower investment yields are computed. At last, the model adjustment parameters such as retirement age and relevant reform measures are analyzed and evaluated.