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. In order to represent the unrestricted reserves value process of this kind of funds, a time homogeneous diffusion stochastic process with finite expected time to ruin is proposed. Then it is projected a financial tool that regenerates the diffusion at some level with positive value every time the diffusion hits a barrier at the origin. So, the financing effort may be modeled as a renewal-reward process if the regeneration level is kept constant. The evaluation of the perpetual maintenance cost expected values and of the finite time period maintenance cost are studied for a concretization of this approach when the unrestricted reserves value process behaves as a generalized Brownian motion process.

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Brownian motion process,diffusion process,first passage time,Pensions fund,Perpetuity,renewal equation

• Mathematics - Natural Sciences
• Economics and Business - Social Sciences