A Stochastic Optimal Growth Model With A Depreciation Factor

This paper is devoted to the study of a one-sector stochastic growth model with the depreciation factor of the output and with bounded and unbounded utility, in which the shocks are allowed to be bounded or unbounded. Our main results are three-fold. Firstly, under a minimal set of assumptions, the Euler equation as well as the existence of a unique continuous optimal policy function for the model is shown to be true. Secondly, under certain assumptions, the existence of an invariant distribution for the output process is confirmed. Finally, we establish the global stability of the optimal output process by showing that the probability density of optimal output converges to a unique invariant density independent of initial output.