In a former paper (Simonovits, 1999), I have discussed the problems of the new Hungarian pension system verbally. In this paper I will present some new results obtained by others and myself with mathematical models, which are related to the Hungarian pension reform (see e.g. Palacios and Rocha, 1998). (1) How can one model a pension system with the life-cycle theory? (Of course, this is introduction rather than new result.) (2) How is the model of a funded system modified if volatility of yields and operating costs are taken into account? (3) What would the actuarially fair model be in an unfunded pension system with flexible age of retirement, and how much saving (and damage) is to be expected from replacing the indexation of pensions in progress to earnings by the combined indexation? (4) How is the efficiency of the pension system affected if the unfunded system is replaced by a partially or fully funded system?