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现收现付制养老保险是一种代际转移的制度,其可持续发展的经济学基础为生产力、工资和人口三者的综合增长因素能够维持代际转移,从而保证人们退休后能够维持稳定的工资替代率。这三种因素的波动形成了一定的风险。如何量化和管理这些风险是本文的研究主题。本文将给出代际人口比例和代际工资比例满足的随机微分方程。基于此,考虑在给定缴费比例和工资替代率条件下,养老保险计划出现支付危机的概率分布。进而,为了寻找风险与收益的平衡,研究现收现付制养老保险的VaR。最后,利用中国的实际统计数据,对本文的理论结果给予实证阐述,并提出应对的策略。
The system of pay-as-you-go pension is a system of intergenerational transfer. Its economic basis for sustainable development is to ensure intergenerational transfer for the integrated growth factor of productivity, wages and population so as to ensure that people can maintain their stability after retirement The wage replacement rate. The fluctuations of these three factors form a certain risk. How to quantify and manage these risks is the subject of this article. This article will give the stochastic differential equations that satisfy the proportion of intergenerational population and the proportion of intergenerational wages. Based on this, we consider the probability distribution of the payment crisis in the pension plan under given contribution rate and salary replacement rate. Furthermore, in order to find the balance between risk and return, we study the VaR of the current pay-as-you-go pension system. Finally, using the actual statistical data in China, this paper gives empirical explanations of the theoretical results and proposes strategies to deal with them.