Pension systems have been expecting projected deficits and governments have been under pressure to increase the statutory retirement age. Fully funded pension system pillars have significant limitations, the recent attempts to adapt social insurance systems have not provided plausible results and empirically have not had strong political support to be fully implemented. Therefore, we created an incentive-based pension system extension that enables a gradual transition to a merit-based pay-as-you-go system. We present a mathematical model based on virtual accumulation of resources that works with full working, relaxed and retired phases, based on the individual decision when to enter them. We present calculations based on the parameters that are valid in the Czech Republic, but the model is designed as a general one, therefore the model variables can be adjusted according to parameters in any country withpublic pension system. Then we discuss the implications and possibilities related to the model, also in the context of changes that we see in the labour market, behavioural patterns of the older generation and the socioeconomic development in the 21st century.

中文翻译：

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现收现付退休金制度的激励性扩展

养老金制度一直预期会出现赤字，政府也面临着提高法定退休年龄的压力。全额养恤金制度的支柱有很大的局限性，最近对社会保险制度进行调整的尝试并未提供合理的结果，而且根据经验，也没有强有力的政治支持予以全面实施。因此，我们创建了基于激励的养老金系统扩展，使之能够逐步过渡到基于绩效的现收现付制。我们提出了一种基于虚拟资源积累的数学模型，该模型可根据进入它们的个人决定，在正常工作，放松和退休阶段工作。我们根据在捷克共和国有效的参数进行计算，但该模型是通用模型，因此，在任何具有公共养老金制度的国家中，模型变量都可以根据参数进行调整。然后，我们在劳动力市场的变化，老一辈的行为模式以及21世纪社会经济发展的背景下，讨论了与该模型相关的含义和可能性。