The situation of some pensions funds that are not appropriately auto financed and are thoroughly maintained with an outside financing effort is considered in this paper. To represent the unrestricted reserves value process of this kind of funds, a time homogeneous diffusion stochastic process is proposed. Then it is projected a financial tool that regenerates the diffusion at some level with positive value. So, the financing effort may be modeled as a renewal-reward process. The relevant costs are studied when the unrestricted reserves value process behaves as a generalized Brownian motion process.

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pensions fund,diffusion process,Brownian motion process,first passage time,perpetuity,renewal equation