The greatest deficit in increasing the dynamics and stability of the economic system is to create incentive and other conditions for extending the time of labour productivity and its utilization in job market. This requires, amongst other things, a fundamental reform of the pension system, based on the precise definition of what an insured event is: not reaching a certain age but the loss of the ability to engage in gainful activity to provide a means of living a dignified life. We propose a general model of gradual reform of the pension system based on voluntary entry into the fully closed and with full merit extension of the current system of pay-as-you-go pension insurance, which exists in the Czech Republic and other countries. Anyone entering this extension after reaching the retirement age gets the payment in the form of life annuities according to what they paid into the system based on the insurance mathematics of the life expectancy. In the paper we present the appropriate economic model. Contrary to previously published outcomes, we also deal with the expenditure side (by drawing resources from this system by older people contrary to the changing needs of living).