The thesis aims to provide a pension reform proposal to the PAYG based Hungarian system that is inspired by the Danish system. Pension systems in general struggle with the problems of demographic changes among others in the 21st century. According to a recent study the Danish system, which functions as a multi-pillar system, is one of the bests globally. On the contrary, the Hungarian pension system operates in a PAYG system since 2011 again and faces severe sustainability and old-age poverty issues. Using the overlapping generations model by Diamond, effects and consequences of longevity and ageing population are discussed in both PAYG and funded systems, assuming favorable results for the latter one. Furthermore, the old-age poverty issue is investigated with the help of income inequality measures. The comparison of the systems and the two countries lead to a proposal incorporating the introduction of a mixed pension combining PAYG and funded schemes.