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This paper adapts an actuarial mathematical model, built for the Italian public pension system, based on the law proposal 3035/2009 to the Accountant Pension Fund (CNPADC). The aim is to introduce a new philosophy pension highly correlated with the concept of adequacy for an ambitious social welfare; using the logic of the 3035/2009 proposal, which guarantees a minimum threshold for the replacement rate of the direct pension, this study provides a rigorous actuarial mathematical model that explains a sort of rate of contribution at a tendential equilibrium, in a pay-as-you-go pension system. This model reveals for which parameters it is possible to intervene to maintain the standard of living in retirement.

An actuarial mathematical model for a new pension philosophy. An application to the accountant pension fund