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.