Pensions funds not auto financed and systematically maintained with an outside financing effort are considered in this work. Representing the unrestricted reserves value process of this kind of funds, a time homogeneous diffusion process with finite expected time till the ruin is proposed. It is also admitted a financial tool that regenerates the diffusion, at some level with positive value every time it hits a barrier at the origin. Then the financing effort may be modeled as a renewal-reward process if the regeneration level is kept constant. The perpetual maintenance cost expected values evaluation and of the finite time period maintenance cost are studied. An application of this approach, when the unrestricted reserves value process behaves as a generalized Brownian motion process, is presented.

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Pensions fund, Diffusion process, First passage times, Renewal equation