Fast growing stochastic dynamics models.

A stochastic intertemporal optimization model with stationary discounted one-period utility and stationary dynamic constraints is studied. The main goal is to extend standard dynamic programming techniques, which require utilities to be bounded, to the case of unbounded utilities. This is possible by imposing a limit on the growth rate of state variables. A relationship between this growth rate and the discount factor is established. These results are then applied to the consumption-saving model with no borrowing.