Massimo Angrisani

Sustainability of a pay-as-you-go pension system by dynamic immigration control

Abstract The sustainability of a pay-as-you-go pension system strongly depends on the underlying demographic process determining the inverse old-age dependency ratio (the proportion of the active subpopulation to pensioners), considered as a sustainability index. Based on the classical Leslie population model, a dynamic demographic model including a controlled immigration is set up. A convergent algorithm is given which steers the population towards a demographic equilibrium with a better sustainability index, and at the same time minimizes the yearly immigration. In addition, simulations are provided for Italian data, comparing the demographic dynamics corresponding to different decision scenarios.

Synthetic approaches to problems of fixed points in metric space

SummaryTwo original synthetic approaches to vast classes of fixed point theorems.

An extension of Aaron’s sustainable rate of return to partially funded pension systems

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 (2006, 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 Aarons 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.

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.

Controlling a demographic wave in defined contribution pension systems

Abstract In several developed countries, the baby boomers will come to retire in the next decades. This problem will threaten the sustainability and the intergenerational 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.