The optimal rate of return for defined contribution pension systems in a stochastic framework

Abstract

This paper deals with the problem of the optimal rate of return to be paid by a defined contribution pension system to its participants’ savings, namely the rate that achieves the goal of the most favorable returns on their contributions jointly with the sustainability of the pension system. We consider defined contribution pension systems provided with a funded component, and for their study we use the “theory of the logical sustainability of pension systems” already developed in several previous works. In this paper, we focus on pension systems in a demographically stable state, whereas the productivity of the active participants and the financial rate of return on the pension system’s fund, rates that constitute the “ingredients” of the optimal rate of return on contributions, are modeled by two stochastic processes. We show that the decisional rule defining the optimal rate of return on contributions is optimal in the sense that it is effective in terms of sustainability, and also efficient in the sense that if the system pays to its participants’ contributions a rate of return that is either higher or lower than the one provided by the rule, then the pension system becomes unsustainable or overcapitalized, respectively.

The Logical Sustainability Theory for pension systems: the discrete-time model in a stochastic framework under variable mortality

“…If the active population is assumed to be constant in year k + 1, then it is σ k+1 = g k+1 , where g k+1 denotes the growth rate of the productivity in year k + 1. Note that the growth rate of wages can be described by a stochastic process as in [9], for example. Equation 9is a linear difference equation, of first order, with variable coefficients, and homogeneous.…”

“…In Sweden, the NDC scheme is supplemented by a proper automatic balance mechanism that adjust benefits when the system turns in a situation estimated to be of financial unsustainability. However, despite what many believe, note that the adoption of the NDC scheme does not guarantee the pension system [9]. This paper is inserted in the framework of the logical sustainability theory, which is substantially based on the two forerunner papers [1,2], where the mathematical formalization of the pension system's structure and the logical management rules that ensure the financial sustainability are set in a "continuous" framework.…”