Deterministic Equivalence in Stochastic Infinite Horizon Problems

We consider a general infinite horizon problem with stochastic data. We establish conditions under which the stochastic problem may be correctly solved using an equivalent deterministic problem. In particular, we establish conditions under which there exists an equivalent interest rate, which permits replacement of the stochastic data by their expectations. This equivalent interest rate can be approximated by a linear function of the ratio of the variance to the mean of the stochastic data. Applications to production planning are included.