On the existence of optimal processes in non-stationary environments

We consider an aggregative model of intertemporal allocation under uncertainty, in which the utility and production functions are allowed to be time dependent, the random shocks occurring in each period are entirely arbitrary, and the production functions are permitted to be non-concave. In this framework, we provide a theorem on the existence of infinite-horizon optimal processes. In the course of establishing this result, we obtain the existence of optimal policy functions and we show that they are monotone in the stock levels.