Some Results on An 'Income Fluctuation Problem'.

A consumer at each period, given the income available, y, has to decide how much to consume and save. If he consumes c or units he gets uc units of satisfaction or utility, and if x y - c or is the amount saved then the available income in the next period is rx omegak where omegak is a random variable, and r is an interest factor that is assumed to be known with certainty. Infinite time horizon problems are considered, and it is shown that if 0 delta r 1, where 0 delta 1 is a discount factor, then the limiting policy is optimal. Questions about the behavior of the stock level are considered, such as boundness and it is given an example that shows that the stock level might converge almost surely to infinity.