Infinite Horizon Investment—Consumption Policies

We consider an infinite horizon investment-consumption problem in which the objective is to mmimize the discounted sum of the one period utilities. The one period utility function is assumed to be concave but may be unbounded. Both the state and action spaces are uncountable. If the average growth rate of assets is less than the reciprocal of the discount rate and if a weak regularity condition is satisfied an optimal stationary policy is shown to exist. Also the optimal return function satisfies the functional equation of dynamic programming and inherits several properties of the one period utility function.