In this paper we develop several financial equilibrium models in a public pensions system. The equality between contributions and pensions in a pure pay-as-you-go scheme is modified with the incorporation of a capital fund; we then obtain a long-term pay-as-you-go scheme. Furthermore, we discuss the desirability of introducing several constraints in the models to take into account social or political limitations. The resultant models are mathematical optimization problems. The solution is the optimal path for the main variables of the system (contribution rate and pension substitution rate) in order to reach a long-term financial equilibrium in the puhlic pensions system with the existing constraints. We solve a model for the Spanish case in the horizon 1995-2030, using macroeconomic scenarios and retirement pensions projections made by the Spanish Ministry of Employment and Social Security.

Keywords: Social Security, pensions, finance, capital funds, dynamic optimization.