Maintenance Problem of Insufficiently Financed Pension Funds -- A Stochastic Approach

TL;DR

This paper models the maintenance of underfunded pension schemes using a stochastic diffusion process, analyzing costs and proposing a renewal-based financial tool to ensure sustainability.

Contribution

It introduces a stochastic diffusion model with regeneration to represent pension fund reserves and evaluates maintenance costs, including an application with generalized Brownian motion.

Findings

Perpetual maintenance costs can be explicitly calculated.

Finite time maintenance costs are derived.

The model applies to generalized Brownian motion processes.

Abstract

The generic case of pensions fund that it is not sufficiently auto financed and it is thoroughly maintained with an external financing effort is considered in this chapter. 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 placed at the origin. So, the financing effort can be modeled as a renewal-reward process if the regeneration level is preserved constant. 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.