This paper analyzes the issue of pension system sustainability in a logical mathematical key with great relevance to the rules of the demographic aspects. A mathematical formalization of a defined contribution pension scheme in a partially funded framework is given. In this framework a demographic representation of pension system collectivity, not based on fictitious assumptions but founded on actual reality, is used. Logical and mathematical conditions of sustainability, which are deduced by evolution equations of differential type, are given to control the pension system financial state.
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