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 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.