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Title Stochastic Optimal Growth with Bounded or�@Unbounded Utility and with Bounded or�@Unbounded Shocks Abstract This paper studies a one-sector stochastic optimal growth model with i.i.d. productivity shocks in which utility is allowed to be bounded or unbounded, the shocks are allowed to be bounded or unbounded, and the production function is not required to satisfy the Inada conditions at zero and infinity. Our main results are threefold. First, we confirm the Euler equation as well as the existence of a continuous optimal policy function under a minimal set of assumptions. Second, we establish the existence of an invariant distribution under quite general assumptions. Third, we show that the output density converges to a unique invariant density independently of initial output under the assumption that the shock distribution has a density whose support is an interval, bounded or unbounded. In addition, we provide existence and stability results for general one-dimensional Markov processes. Keywords: Stochastic growth; Unbounded utility; Bounded or unbounded shocks; Markov processes; Existence and stability of a invariant distribution JEL Classification: C61; C62; E32; O41 Takashi KAMIHIGASHI Research Institute for Economics and Business AdministrationKobe UniversityRokkodai-cho, Nada-ku, Kobe 657-8501 JapanPhone: (81) 78 803 7036 Fax: (81) 78 803 7059