An overlapping generations model of social security with shocks to the productivity of labor and capital and demographic shocks is studied. We focus attention on stationary long run allocations. An allocation is if there does not exist another feasible allocation that improves the expected welfare of all generations, computed conditionally on the state of the world when they are born. We characterize the set of interim optimal allocations and study the equilibria associated with various institutional forms of social security from the point of view of this optimality criterion. We obtain the analogs of the two traditional welfare theorems of microeconomic theory. Assume that there exists a financial asset in fixed quantity, which supports some (non null) intergenerational transfers. Then the rational expectations equilibrium allocation of this economy is interim optimal. Conversely, any stationary interim optimal allocation can be supported by such an equilibrium, with adequate lump sum transfers.