In this paper we explore the computation and simulation of stochastic overlapping generation (OLG) models. To do so we compute all Markovian equilibria adopting a recently developed numerical algorithm. Among the models we studied, the indeterminacy in deterministic OLG model results in many different equilibrium paths corresponding to the initial condition that all asymptotically converge to the same steady state. The uncertainty introduces indeterminacy with infnite dimension due to the existence of numerous selections of transition and policy functions from the equilibrium set. Each selection correspondences a sequential competitive equilibrium that may present excessive volatile movements in asset price. It is possible to construct a continuum of recursive equilibrium. However our numerical simulations suggest that it is problematic to look at recursive equilibrium in which the volatility of asset price is solely determined by the distribution of the shock.