The sustainability of defined contribution pension schemes with a funded component is studied under the assumption of a constant contribution rate. To this aim, we use the new methodology introduced in Angrisani (2006Angrisani ( , 2008 for the analysis and the management of partially funded pension systems: assuming the rule on the rate of return on the pension liability and by means of the necessary and sufficient condition of sustainability stated in the previous cited references, we provide a new theorem for the defined contribution pension schemes with a funded component; it establishes a necessary condition for the sustainability under hypotheses of general stabilisation and constant contribution rate. The Aaron's rule on the sustainable rate of return for unfunded pension schemes constitutes a particular case of the rule on the sustainable rate of return for partially funded pension systems used in our theorem.

In several developed countries, the baby boomers will come to retire in the next decades. This problem will threaten the sustainability and the inter- generational equity of mandatory pay-as-you-go pension systems because they will have to drain the “demographic wave” of retirees with a relatively small number of contributors. In this paper, we give the operating method developed on the basis of a general principle, which a defined contribution pension system, in a state of stable sustainability, should adopt to control these issues in the presence of a demographic wave. In the theoretical profile, our approach breaks and overcomes the classical juxtaposition between funded and pay-as-you-go pension schemes, carrying out the integration of the two financial methods

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 aim of this work is to provide the logical sustainability model for defined contribution pension systems (see [1], [2]) in the discrete framework under stochastic financial rate of the pension system fund and stochastic productivity of the active participants. In addition, the model is developed in the assumption of variable mortality tables.Under these assumptions, the evolution equations of the fundamental state variables, the pension liability and the fund, are provided. In this very general discrete framework, the necessary and sufficient condition of the pension system sustainability, and all the other basic results of the logical sustainability theory, are proved.In addition, in this work new results on the efficiency of the rule for the stabilization over time of the level of the unfunded pension liability with respect to wages, level that is defined as β indicator, are also proved.

Many countries are facing up to the problem of the financial sustainability of their pension systems by the transition from the defined benefit scheme to the defined contribution one. However, the defined contribution formula alone does not guarantee sustainability. There are many economic, financial and demographic factors to be taken into consideration, the first of which being the rate of return to be paid on contributions and benefits. This article deals with the shift to the defined contribution scheme in contexts of economic and demographic instability, in which the steady state does not occur substantially, with reference to one of the largest Italian statutory pension systems for professional workers. We propose a new way to structure and manage a pension system on the basis of a general principle, we also provide a proper rule for the rate of return on the pension liability as well as a pension indexation rule differentiated for both defined contribution and defined benefit pensions in order to improve intergenerational equity.