Finding solutions to the Bellman equation relies on restrictive boundedness assumptions. The literature on endogenous growth or business cycle models with unbounded random shocks provide with numerous examples of recursive programs in which returns are not bounded along feasible paths. In this...

Finding solutions to the Bellman equation often relies on restrictive boundedness assumptions. In this paper we develop a method of proof that allows to dispense with the assumption that returns are bounded from above. In applications our assumptions only imply that long run average (expected)...