This article addresses the issue of the sustainability of a public PAYG pension scheme. It presents a mixed model, with the introduction of a funded component to balance the PAYG part when the ratio contributors- pensioners is decreasing. The aim of the work is to manage the funding of a public pension system. Stochastic risk indicators are presented to assess the sustainability of the scheme. We find the optimal share to invest in funding as minimize the probability of default of the system. Finally we analyse how this share varies when there is a decreasing in the number of the contributors.