Equilibrium and Maintenance Costs of Pensions Funds Studied through Stochastic Processes

In this study, a representation is depicted of a pension fund through a stochastic network with two infinite servers’ nodes. With this representation, it is allowed to deduce an equilibrium condition of the system with a basis on the identity of the random rates expected values, for which the contributions arrive at the fund and the pensions are paid by the fund. Then, to address situations of imbalance, the generic case of a pension fund that is not sufficiently auto-financed, and is thoroughly maintained with an external financing effort is considered in this chapter. To represent the unrestricted reserves value process of this kind of fund, 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 a positive value every time the diffusion hits a barrier placed at the origin. So, the financing effort can be modeled as a renewal-reward process if the regeneration level is preserved constantly. The perpetual maintenance cost expected values and the finite-time maintenance cost evaluations are studied. An application of this approach when the unrestricted reserves value process behaves as a generalized Brownian motion process is presented.