There are three main challenges facing pay-as-you-go public pension systems. First, pension systems need to provide an adequate income for pensioners in the retirement phase. Second, participants wish a fair level of benefits in relation to the contributions paid. Last but not least, the pension system needs to be financially sustainable in the long run. In this paper, we jointly analyse the adequacy, fairness and sustainability of both defined benefit and defined contribution schemes. Finally, risk sharing mechanisms, that involve changes in the key variables of the system, are designed to restore the financial sustainability while we study their consequences on the adequacy and fairness of the system.

The aim of this article is twofold: to establish the connection between the ‘Contribution Asset’ (CA) and the ‘Hidden Asset’ (HA) and to determine whether using either of them to compile the Actuarial Balance (AB) sheet in the Pay-As-You-Go (PAYG) pension system will provide a reliable solvency indicator. With these aims in mind, we develop a model based on those first put forward by Settergren and Mikula (2005) and Boado-Penas et al. (2008) to obtain the analytical properties of the CA and to confirm its soundness as a measure of the assets of a PAYG scheme. Our model also enables us to explore whether, and to what extent, the HA can be considered a second alternative measure of the assets for PAYG schemes. The main theoretical finding is that, despite their very different natures, the HA and the CA may nearly coincide at the limit when the interest rate of the financial market approaches the growth of the covered wage bill from above, but the HA supplies a solvency indicator which is not always consistent with the system's financial health.